Abstract
Let \( {\mathfrak{M}} \) be a set of finite groups. Given a group \( G \), denote the set of all subgroups of \( G \) isomorphic to the elements of \( {\mathfrak{M}} \) by \( {\mathfrak{M}}(G) \). A group \( G \) is called saturated by groups in \( {\mathfrak{M}} \) or by \( {\mathfrak{M}} \) for brevity, if each finite subgroup of \( G \) lies in some element of \( {\mathfrak{M}}(G) \). We prove that every locally finite group \( G \) saturated by \( {\mathfrak{M}}=\{GL_{m}(p^{n})\} \), with \( m>1 \) fixed, is isomorphic to \( GL_{m}(F) \) for a suitable locally finite field \( F \).
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The author was supported by the Russian Science Foundation (Grant 19–71–10017).
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Shlepkin, A.A. Locally Finite Groups with Prescribed Structure of Finite Subgroups. Sib Math J 62, 182–188 (2021). https://doi.org/10.1134/S0037446621010201
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DOI: https://doi.org/10.1134/S0037446621010201