Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group

For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore uniquely determined by the set μ(G) consisting of elements of ω(G) that are maximal with respect to divisibility. We prove that a finite group isospect...

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Bibliographic Details
Published in:Algebra and logic 2023-03, Vol.62 (1), p.50-53
Main Authors: Zhurtov, A. Kh, Lytkina, D. V., Mazurov, V. D.
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Finite groups
Group theory
Isomorphisms (Mathematics)
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
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Summary:For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore uniquely determined by the set μ(G) consisting of elements of ω(G) that are maximal with respect to divisibility. We prove that a finite group isospectral to Aut(J 2 ) is unsolvable.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-023-09723-0