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This article is cited in 2 scientific papers (total in 2 papers)
On the periodic groups saturated with finite simple groups of lie type b3
D. V. Lytkinaab, V. D. Mazurovc a Siberian State University of Telecommunications and Informatics, Novosibirsk
b Novosibirsk State University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
Let \gothM be a set of finite groups. Given a group G, denote by \gothM(G) the set of all subgroups of G isomorphic to the elements of \gothM. A group G is said to be saturated with groups from \gothM (saturated with \gothM, for brevity) if each finite subgroup of G lies in an element of \gothM(G). We prove that a periodic group G saturated with \gothM={O7(q)∣q≡±3(mod8)} is isomorphic to O7(F) for some locally finite field F of odd characteristic.
Keywords:
periodic group, group of Lie type, orthogonal group, group saturated with a set of groups.
Received: 17.01.2020 Revised: 17.01.2020 Accepted: 19.02.2020
Citation:
D. V. Lytkina, V. D. Mazurov, “On the periodic groups saturated with finite simple groups of lie type b3”, Sibirsk. Mat. Zh., 61:3 (2020), 634–640; Siberian Math. J., 61:3 (2020), 499–503
Linking options:
https://www.mathnet.ru/eng/smj6006 https://www.mathnet.ru/eng/smj/v61/i3/p634
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