Abstract: Given a finite group L, let N(L) denote the set of its conjugacy class sizes. Let X and Y be sets of natural numbers, G be a finite group such that N(G) = X ×Y. In the article [16] the question is formulated: for which sets X and Y is it true that G ≃A×B, where N(A) = X and N(B) = Y? More than 30 years ago, J. Thompson formulated a conjecture that any finite simple group is uniquely determined by its set of sizes of conjugacy classes in the class of finite groups with trivial center. In 2019, the validity of this conjecture was proven. In 2020, it was noted that in addition to simple groups, some direct products of simple groups are also determined by this set. We prove that if N(G) = N(Altp ×Alt5), where p is a prime greater than 1361 and the group G has a trivial center, then G ≃ Alt5 ×Altp.

Cite: Gorshkov I.B. , Shepelev V.D.
N-recognizability of Groups Altp ×Alt5, Where p >1361 Is a Prime Number
Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics). 2026. V.55. P.110-122. DOI: 10.26516/1997-7670.2026.55.110 РИНЦ OpenAlex

Dates:

Submitted:	Mar 26, 2025
Accepted:	Jun 17, 2025
Published online:	Mar 16, 2026

Identifiers:

≡ Elibrary:	89000289
≡ OpenAlex:	W7134931589

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