On Periodic Groups Isospectral to \( A_{7} \). II

Abstract

Let \( G \) be a periodic group and let \( \omega(G) \) be the spectrum of \( G \). We prove that if \( G \) is isospectral to \( A_{7} \), the alternating group of degree \( 7 \) (i.e., \( \omega(G) \) is equal to the spectrum of \( A_{7} \)); then \( G \) has a finite nonabelian simple subgroup.

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Funding

The first author was supported by the Russian Foundation for Basic Research (Grant 18–31–20011).

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Correspondence to A. S. Mamontov.

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Mamontov, A.S., Jabara, E. On Periodic Groups Isospectral to \( A_{7} \). II. Sib Math J 61, 1093–1101 (2020). https://doi.org/10.1134/S0037446620060105

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Keywords

  • periodic group
  • locally finite group
  • spectrum

UDC

  • 517.518.85