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Recognizing \(A_7\) by its set of element orders. (English. Russian original) Zbl 07304937
Sib. Math. J. 62, No. 1, 93-104 (2021); translation from Sib. Mat. Zh. 62, No. 1, 117-130 (2021).
Summary: Let \(G\) be a periodic group, and let \(\omega(G)\subseteq{ \mathbb{N} }\) be the spectrum of \(G\) that is the set of orders of elements in \(G \). We prove that the alternating group \(A_7\) is uniquely recognized by its spectrum in the class of all groups.
MSC:
20D Abstract finite groups
20G Linear algebraic groups and related topics
Software:
GAP
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References:
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