Abstract:
In the paper, on the basis of the notion of saturation introduced in [1], we give a characterization of locally finite simple groups Re(P), Sz(Q) and L2(P) with an Abelian Sylow 2-subgroup in the classes of mixed and periodic groups. A part of the main results was announced in [2]. Theorem 2 of the paper generalizes results of [3, 4].
Citation:
A. I. Sozutov, A. K. Shlepkin, “On Some Groups with Finite Involution Saturated with Finite Simple Groups”, Mat. Zametki, 72:3 (2002), 433–447; Math. Notes, 72:3 (2002), 398–410
\Bibitem{SozShl02}
\by A.~I.~Sozutov, A.~K.~Shlepkin
\paper On Some Groups with Finite Involution Saturated with Finite Simple Groups
\jour Mat. Zametki
\yr 2002
\vol 72
\issue 3
\pages 433--447
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\crossref{https://doi.org/10.4213/mzm434}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1963170}
\zmath{https://zbmath.org/?q=an:1050.20027}
\transl
\jour Math. Notes
\yr 2002
\vol 72
\issue 3
\pages 398--410
\crossref{https://doi.org/10.1023/A:1020507606449}
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Linking options:
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https://doi.org/10.4213/mzm434
https://www.mathnet.ru/eng/mzm/v72/i3/p433
This publication is cited in the following 11 articles:
A. I. Sozutov, “Groups Saturated with Finite Frobenius Groups”, Math. Notes, 109:2 (2021), 270–279
A. I. Sozutov, “On groups with a strongly embedded unitary subgroup”, Sib. elektron. matem. izv., 17 (2020), 1128–1136
D. V. Lytkina, V. D. Mazurov, “Characterization of simple symplectic groups of degree 44 over locally finite fields of characteristic 22 in the class of periodic groups”, Siberian Math. J., 58:5 (2017), 850–858
D. V. Lytkina, V. D. Mazurov, “Periodicheskie gruppy, nasyschennye konechnymi prostymi gruppami”, Tr. In-ta matem., 23:2 (2015), 72–75
K. A. Filippov, “On periodic groups saturated by finite simple groups”, Siberian Math. J., 53:2 (2012), 345–351
Filippov K.A., “Gruppy s usloviyami nasyschennosti”, Matematicheskii forum (itogi nauki. yug Rossii), 6 (2012), 155–164
Groups with saturation properties
D. V. Lytkina, “On the periodic groups saturated by direct products of finite simple groups”, Siberian Math. J., 52:2 (2011), 267–273
A. A. Kuznetsov, K. A. Filippov, “Gruppy, nasyschennye zadannym mnozhestvom grupp”, Sib. elektron. matem. izv., 8 (2011), 230–246
D. V. Lytkina, V. D. Mazurov, “Groups containing a strongly embedded subgroup”, Algebra and Logic, 48:2 (2009), 108–114
V. I. Senashov, A. I. Sozutov, V. P. Shunkov, “Investigation of groups with finiteness conditions in Krasnoyarsk”, Russian Math. Surveys, 60:5 (2005), 805–848
A. G. Rubashkin, K. A. Filippov, “Periodic groups saturated with the groups L2(pn)L2(pn)”, Siberian Math. J., 46:6 (2005), 1119–1122