Abstract
Let An denote the alternating group of degree n. Consider a group G whose spectrum, i.e. the set of element orders, equals the spectrum of A7. Assume that G has a subgroup H isomorphic to A4 whose involutions are squares of elements of order 4. Then either O2(H) ⊆ O2(G)or G has a nonabelian finite simple subgroup.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 137–147.
The author was supported by the Russian Science Foundation (Grant 14-21-00065).
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Mamontov, A.S. On Periodic Groups Isospectral to A7. Sib Math J 61, 109–117 (2020). https://doi.org/10.1134/S0037446620010097
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DOI: https://doi.org/10.1134/S0037446620010097