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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
##### Keywords:
periodic group; locally finite group; spectrum
GAP
Full Text:
##### References:
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