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This article is cited in 2 scientific papers (total in 2 papers)
Locally finite groups with prescribed structure of finite subgroups
A. A. Shlepkin Siberian Federal University, Krasnoyarsk, Russia
Abstract:
Let M be a set of finite groups. Given a group G, denote the set of all subgroups of G isomorphic to the elements of M by M(G). A group G is called saturated by groups in M or by M for brevity, if each finite subgroup of G lies in some element of M(G). We prove that every locally finite group G saturated by M={GLm(pn)}, with m>1 fixed, is isomorphic to GLm(F) for a suitable locally finite field F.
Keywords:
locally finite group, general linear group, saturation.
Received: 13.06.2020 Revised: 31.08.2020 Accepted: 09.10.2020
Citation:
A. A. Shlepkin, “Locally finite groups with prescribed structure of finite subgroups”, Sibirsk. Mat. Zh., 62:1 (2021), 226–234; Siberian Math. J., 62:1 (2021), 182–188
Linking options:
https://www.mathnet.ru/eng/smj7552 https://www.mathnet.ru/eng/smj/v62/i1/p226
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Abstract page: | 311 | Full-text PDF : | 70 | References: | 70 | First page: | 16 |
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