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 4 over locally finite fields of characteristic 2 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)”, Siberian Math. J., 46:6 (2005), 1119–1122