Reversed and remanded with instructions by published opinion. Judge[*625] WILLIAMS wrote the opinion, in which Chief Judge WILKINS and Judge MICHAEL joined.

OPINION

Richard and Lillie Long (the Longs), signatories to a contract containing an arbitration clause, sued American Bankers Insurance Group (ABIG), a nonsignatory to the contract, on claims relating to a promissory note issued to the Longs. ABIG filed a petition in the district court seeking to compel the Longs to arbitrate their claims, and the district court denied the petition. For the reasons that follow, we reverse.

I.

On December 9, 2003, the Longs filed a class-action suit in the Richland County (South Carolina) Court of Common Pleas against ABIG and others alleging that ABIG participated in a scheme to defraud investors through the sale of worthless securities. In particular, the Longs’ complaint alleged that Thaxton Life Partners (TLP) sold automobile insurance policies underwritten by ABIG to the general public and that because ABIG did not have enough funds to pay claims on the policies, it persuaded TLP to offer approximately $18 million of worthless promissory notes to the public to fund the insurance. As part of its fraudulent scheme, ABIG, knowing that TLP would be unable to pay the promissory notes, structured them so that it (ABIG) was in the position of first priority in the event of a default.

The Longs’ complaint further alleges that on or about August 19, 2003, the Longs purchased a $75,000 promissory note (the Note) from TLP for a one-year term with a promised return of 10%. The Note was appended to and its terms “incorporated ... by reference” in a document entitled “Form of Senior Subordinated Term Note Subscription Agreement” (Subscription Agreement). (J.A. at 11.) The Subscription Agreement contained an arbitration clause providing “that any dispute, controversy or claim arising out of or in connection with, or relating to, any subscription of the Note, or any breach or alleged breach hereof, including allegations of violations of federal or state securities law” shall be subject to arbitration. (J.A. at 14.) The Longs and TLP were signatories to the Subscription Agreement; ABIG was not. TLP later filed for bankruptcy protection in the Bankruptcy Court for the Middle District of North Carolina, and it informed the Longs and other investors that it would neither pay interest on the promissory notes nor return the principal investments.

The Longs’ state-court complaint alleges eleven individual and class causes of action against ABIG arising out of its alleged participation in the fraudulent promissory-note scheme: (1) interference with contract, (2) securities fraud, (3) negligence, (4) equitable subordination, (5) civil conspiracy, (6) unjust enrichment, (7) respondeat superior, (8) rescission, (9) participation and alter ego, (10) violation of the South Carolina Unfair Trade Practices Act (SCUTPA), and (11) aiding and abetting. In essence, these causes of action seek recovery for: (1) ABIG’s alleged interference with TLP’s obligations under the notes (interference with contract claim); (2) ABIG’s alleged failure to disclose that TLP would be unable to pay the notes (securities fraud and negligence claims); (3) ABIG’s alleged conspiracy with, and control over, TLP in issuing the notes and in insuring that TLP did not make payments thereon (civil conspiracy); (4) ABIG’s allegedly unlawful retention of the proceeds from the notes (unjust enrichment and rescission claims); and (5)[*626] ABIG’s alleged unfair trade practices regarding the notes (SCUTPA claim). ^[1] The Longs seek to recover from ABIG actual damages, punitive damages and/or treble damages, rescission of the notes, a declaratory judgment subordinating ABIG’s interest in the notes, and attorney’s fees and costs. The Longs did not name TLP as a party to the suit.

After the Longs filed their complaint, ABIG removed the suit to the bankruptcy court where TLP’s bankruptcy proceeding was pending, but the bankruptcy court remanded to state court. On August 5, 2004, ABIG filed a petition to compel arbitration against the Longs in the District Court for the District of South Carolina, see 9 U.S.C.A. § 4 (West 1999) (providing that “[a] party aggrieved by the alleged failure, neglect, or refusal of another to arbitrate under a written agreement for arbitration may petition any United States district court which, save for such agreement, would have jurisdiction under Title 28, in a civil action or in admiralty of the subject matter of a suit arising out of the controversy between the parties, for an order directing that such arbitration proceed in the manner provided for in such agreement”), contending that it (ABIG) was entitled to enforce the arbitration clause in the Subscription Agreement despite the fact it was not a signatory thereto. In support of this contention, ABIG argued, inter alia, that the Longs should be equitably estopped from ai’guing that it was not a signatory to the arbitration clause because each of the Longs’ individual causes of action in their underlying complaint relied on the terms of the Note, which, as discussed, was incorporated by reference into the Subscription Agreement (which, as also discussed, contained the arbitration clause). The district court, which had subject-matter jurisdiction over the petition, see 28 U.S.C.A. § 1332 (West Supp.2005) (providing that “[t]he district courts shall have original jurisdiction of all civil actions where the matter in controversy exceeds the sum or value of $75,000, exclusive of interest and costs, and is between ... citizens of different States”), denied the petition, holding that the Longs were not equitably estopped from asserting that ABIG was not a signatory to the arbitration clause because their individual causes of action in the underlying complaint were based on theories of liability other than breach of the obligations on the Note.

ABIG timely noted an appeal. We have jurisdiction under 9 U.S.C.A. § 16 (West 1999) (“An appeal may be taken from ... an order ... denying a petition under section 4 of this title.... ”).

II.

ABIG makes the same argument on appeal that it made to the district court; viz., that the Longs should be equitably es-topped from arguing that it (ABIG) was not a signatory to the arbitration clause because each of the Longs’ individual causes of action in their underlying complaint relied on the terms of the Note. We agree with ABIG. ^[2] Before explaining why, however, we first discuss the legal principles governing when a non-signatory to an arbitration clause may bind a signatory to arbitration.

A.

As a general matter, “arbitration is a matter of contract [interpretation] and[*627] a party cannot be required to submit to arbitration any dispute which he has not agreed so to submit.” Int'l Paper Co. v. Schwabedissen Maschinen & Anlagen GMBH, 206 F.3d 411, 416 (4th Cir.2000). It is well-established, however, that a non-signatory to an arbitration clause may, in certain situations, compel a signatory to the clause to arbitrate the signatory’s claims against the nonsignatory despite the fact that the signatory and nonsignatory lack an agreement to arbitrate.

One such situation exists when the signatory is equitably estopped from arguing that a nonsignatory is not a party to the arbitration clause. “Equitable estoppel precludes a party from asserting rights he otherwise would have had against another when his own conduct renders assertion of those rights contrary to equity.” Int’l Paper, 206 F.3d at 417-18 (internal quotation marks omitted). “In the arbitration context, the doctrine recognizes that a party may be estopped from asserting that the lack of [another’s] signature on a written contract precludes enforcement of the contract’s arbitration clause when [the party] has consistently maintained that other provisions of the same contract should be enforced to benefit him.” Id. at 418.

Applying these concepts, we have announced the following test for determining when equitable estoppel applies against a signatory to an arbitration clause:

[E]quitable estoppel applies when the signatory to a written agreement con-taming an arbitration clause must rely on the terms of the ... agreement in asserting its claims against the nonsignatory. When each of a signatory’s claims against a nonsignatory makes reference to or presumes the existence of the written agreement, the signatory’s claims arise out of and relate directly to the written agreement, and arbitration is appropriate.

Brantley v. Republic Mortgage Ins. Co., 424 F.3d 392, 395-96 (4th Cir.2005) (quoting MS Dealer Serv. Corp. v. Franklin, 177 F.3d 942, 948 (11th Cir.1999))(alterations, ellipses, and internal quotation marks omitted). ^[3] Because this legal test examines the nature of the signatory’s underlying allegations against the nonsignatory, courts should examine the underlying complaint to determine whether estoppel should apply. See id. at 396 (denying application of estoppel where the signatory-plaintiffs’ underlying “claims” did not rely on the contract containing the arbitration clause).

The “legal principle [underlying the theory of equitable estoppel] rests on a simple proposition: it is unfair for a party to rely on a contract when it works to its advantage, and repudiate it when it works to its disadvantage.” Wachovia Bank, Nat. Ass’n v. Schmidt, 445 F.3d 762, 769 (4th Cir.2006) (internal quotation marks and alterations omitted). To be equitably estopped from denying the applicability of an arbitration clause, therefore, the signatory need not necessarily assert a cause of action against the nonsignatory for breach of the contract containing the arbitration[*628] clause. Instead, estoppel is appropriate if “in substance [the signatory’s underlying] complaint [is] based on the [nonsignatory’s] alleged breach of the obligations and duties assigned to it in the agreement,” Sunkist Soft Drinks, Inc. v. Sunkist Growers, Inc., 10 F.3d 753, 757 (11th Cir.1993) (discussing Hughes Masonry Co. v. Greater Clark County Sch. Bldg. Corp., 659 F.2d 836 (7th Cir.1981)), “regardless of the legal label assigned to the claim,” J.J. Ryan & Sons, Inc. v. Rhone Poulenc Textile, S.A., 863 F.2d 315, 319 (4th Cir.1988). See also R.J. Griffin & Co. v. Beach Club II Homeowners Ass’n, Inc., 384 F.3d 157, 164 (4th Cir.2004) (stating that a party “may [not] use artful pleading to avoid arbitration”).

Although not directly relevant here, it is also important to note that just as estoppel can apply against a signatory to an arbitration clause who sues a nonsignatory thereto, it can also apply against a nonsignatory who sues a signatory. See, e.g., R.J. Griffin, 384 F.3d at 160-64; ^[4] Int'l Paper, 206 F.3d at 416-18. In such a situation, however, we have stated, in language different from Brantley’s “rely on” test, that a non-signatory will be estopped when his underlying claims seek a “direct benefit” from the contract containing the arbitration clause, R.J. Griffin, 384 F.3d at 162. Although R.J. Griffin’s language is different from Brantley’s, the “direct benefit” test, similar to the “rely on” test, recognizes that a nonsignatory should be estopped from denying that it is bound by an arbitration clause when its claims against the signatory “arise[ ] from” the contract containing the arbitration clause. Id. 5

With these principles in mind, we return to ABIG’s argument.

B.

ABIG argues that the Longs should be estopped from arguing that it is not a signatory to the arbitration clause because the Longs’ individual claims rely on the terms of the Note and, because the Note is incorporated by reference into the Subscription Agreement, the Longs are inequitably seeking both to enforce the duties created by the Subscription Agreement and deny the Subscription Agreement’s arbitration clause. In response, the Longs argue that equitable estoppel should not apply because their individual claims were based on theories of liability other than breach of the Note.

[*629] We generally review de novo the district court’s decision on a petition to compel arbitration. Long, 248 F.3d at 315. When, however, the district court’s decision is based on principles of equitable estoppel, we review the district court’s decision for abuse of discretion. See Brantley, 424 F.3d at 395. The district court abuses its discretion when it commits an error or law or clearly errs in making a finding of fact. See Thorn v. Jefferson-Pilot Life Ins. Co., 445 F.3d 311, 317 (4th Cir.2006); Hill v. G.E. Power Sys., Inc., 282 F.3d 343, 348 (5th Cir.2002).

In support of ABIG’s contention that the Longs are equitably estopped from arguing that it is a nonsignatory to the arbitration clause, ABIG contends that when, as here, a nonsignatory to a contract containing an arbitration clause is seeking to es-top a signatory, Brantley’s “rely on” test — • not the “direct benefit” test applied in R.J. Griffin — should apply, and that the “rely on” test is less exacting than the “direct benefit” test. While the Longs do not contest ABIG’s argument that Brantley’s “rely on” test is less exacting than R.J. Chiffin’s “direct benefit” test, they contend that R.J. Griffin’s “direct benefit” test applies both when a signatory is attempting to estop a nonsignatory and when a non-signatory is attempting to estop a signatory.

It is true, as ABIG points out, that our cases have applied Brantley’s “rely on” test when the issue was whether a signatory to the contract containing the arbitration clause should be estopped, Schmidt, 445 F.3d at 769-771; Brantley, 424 F.3d at 396, and R.J. Griffin’s “direct benefit” test when the issue was whether a nonsignatory to the contract should be estopped, see R.J. Griffin, 384 F.3d at 166; Int’l Paper, 206 F.3d at 418. Where, as here, however, the issue is whether the underlying claims are such that the party asserting them should be estopped from denying the application of the arbitration clause, any difference in the two tests is more semantic than substantive. Both tests examine whether the plaintiff has asserted claims in the underlying suit that, either literally or obliquely, assert a breach of a duty created by the contract containing the arbitration clause. Compare Brantley, 424 F.3d at 396 (noting that equitable estoppel applies when the signatory’s claims “arise out of’ the contract containing the arbitration clause (internal quotation marks omitted)) with R.J. Griffin, 384 F.3d at 162 (noting that equitable estoppel does not apply when the nonsignatory sues on theories that “arise from” tort law, not the contract containing the arbitration clause). Whether such examination is called a “direct benefit” test or a “rely on” test, the inquiry is ultimately the same.

ABIG next contends that even if the “rely on” and “direct benefit” tests are identical for purposes of this case, estoppel is proper here because the Longs’ individual claims essentially allege that the duties created by the Note were breached. The Longs argue that estoppel is not proper because they do not assert a claim for breach of the Note.

In support of their counter-argument, the Longs point to R.J. Griffin. There, a builder had entered into a contract containing an arbitration clause with the landowner to build condominiums. 384 F.3d at 159. After the landowner sold the individual units, the new unit owners complained that the units leaked water, and they sued the builder in state court for negligence and breach of the implied warranty of good workmanship. Id. The builder filed a petition to compel arbitration of the owners’ lawsuit, asserting that the owners should be equitably estopped from claiming that the arbitration clause did not apply to them because their state-court[*630] claims depended on the existence of the contract containing the arbitration clause. Id. at 160. On appeal of the district court’s denial of the petition, we rejected this argument, concluding that the owners’ underlying suit did not seek a “direct benefit” from the contract, id. at 161, ^[6] because their negligence- and warranty causes of action were not based on any breach of the contract, but were instead based on duties created by state tort law. Id. at 162-63. The Longs argue that, like the owners in R.J. Griffin, their underlying complaint does not allege that ABIG breached a duty created by the Note.

We disagree. The Longs’ underlying complaint is different from the owners’ complaint in R.J. Griffin in a significant way. In R.J. Griffin, the duties that the builder owed the owners (and allegedly breached by the faulty construction of the condominiums) were created entirely by state tort law; if the builder and landowner had never entered into the building contract, the builder still could have been liable in tort to the owners. Id. Here, by contrast, if TLP had never issued the Note, the Longs would have no basis for recovery against ABIG. Each of the Longs’ individual claims — interference with contract, securities fraud and negligence, civil conspiracy, unjust enrichment and rescission, and violation of SCUTPA— are dependent upon their allegation that ABIG breached a duty created “solely by [the Note]”, id. at 164, for without the alleged breach of the Note, the Longs would have no cause to complain. And although each of the Longs’ individual claims is phrased in tort, the Longs “may [not] use artful pleading to avoid arbitration,” because, at root, those claims attempt “to hold [ABIG] to the terms of [the Note].” Id.

Accordingly, we conclude that the Longs’ individual claims “rely on” the terms of Note, Brantley, 424 F.3d at 395, and that because the Note was incorporated into the Subscription Agreement, it would be inequitable to allow the Longs to seek recovery on their individual claims and at the same time deny that ABIG was a party to the Subscription Agreement’s arbitration clause. The district court made a legal error in concluding otherwise, and it thereby abused its discretion.

III.

Although the Longs are equitably es-topped from arguing that ABIG is not a party to the arbitration clause, estoppel does not preclude a party from making the quite different argument that its claims do not fall within the scope of the arbitration clause. Nevertheless, our conclusion that the Longs’ underlying complaint “rel[ies] on” the Subscription Agreement, Brantley, 424 F.3d at 395, forecloses any argument that the Longs’ claims do not fall within the scope of the arbitration clause, see Am. Recovery Corp. v. Computerized Thermal Imaging, Inc., 96 F.3d 88, 93 (4th Cir.1996) (noting that similarly-worded arbitration clause encompassed all disputes having a “significant relationship” to the contract in which the arbitration clause is contained).

IV.

For the foregoing reasons, we reverse and remand for further proceedings consistent with this opinion

[*631] REVERSED AND REMANDED WITH INSTR UCTIONS.