Recognizability of the Groups PSp8(7m) by the Set of Element Orders

Recognizability of the Groups PSp8(7m) by the Set of Element Orders Full article

Journal

Mathematical Notes
ISSN: 0001-4346 , E-ISSN: 1573-8876

Output data

Year: 2025, Volume: 117, Number: 3-4, Pages: 538-546 Pages count : 9 DOI: 10.1134/s0001434625030198

Tags

orders of elements, simple group, symplectic group, orthogonal group, representations in defining characteristic.

Authors

Grechkoseeva M.A. ¹

Affiliations

1	Sobolev Institute of Mathematics

The set of orders of the elements of a finite group G is called the spectrum of G. A group G is said to be unrecognizable by spectrum if there are infinitely many pairwise nonisomorphic finite groups that have the same spectrum as G. There is a conjecture that every finite simple classical group unrecognizable by spectrum is contained in the following list: PSL3(3), PSU3(q), PSU5(2), PSp4(q), PSp8(q), and PΩ9(q). The only groups in this list that were not known to be unrecognizable by spectrum are PSp8(7m). In the present paper, it is shown that PSp8(7m) are not unrecognizable and, moreover, any of these groups is uniquely (up to isomorphism) determined by its spectrum in the class of all finite groups.

Grechkoseeva M.A.
Recognizability of the Groups PSp8(7m) by the Set of Element Orders
Mathematical Notes. 2025. V.117. N3-4. P.538-546. DOI: 10.1134/s0001434625030198 Scopus OpenAlex

Гречкосеева M.A.
Распознаваемость групп PSp8(7m) по множеству порядков элементов
Математические заметки. 2025. Т.117. №4. С.494-504. DOI: 10.4213/mzm14506 РИНЦ OpenAlex

Submitted:	Jun 10, 2024
Accepted:	Sep 10, 2024
Published print:	Jun 16, 2025
Published online:	Jun 16, 2025

Scopus:	2-s2.0-105008202704
OpenAlex:	W4411339411

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