Abstract:
The characterization of finite simple groups with the Dπ propert for any set π of odd prime numbers is completed. It was proved earlier that a finite group has the Dπ property if and only if each of its composition factors has this property, hence the results of the paper provide an exhaustive characterization of the Dπ property for all finite groups with known composition factors in the case 2∉π.
Citation:
D. O. Revin, “The Dπ property of finite groups in the case 2∉π”, Группы и графы, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 1, 2007, 166–182; Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S164–S180
\Bibitem{Rev07}
\by D.~O.~Revin
\paper The $D_\pi$ property of finite groups in the case $2\notin\pi$
\inbook Группы и графы
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 1
\pages 166--182
\mathnet{http://mi.mathnet.ru/timm80}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2338248}
\elib{https://elibrary.ru/item.asp?id=12040761}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2007
\vol 257
\issue , suppl. 1
\pages S164--S180
\crossref{https://doi.org/10.1134/S0081543807050124}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547657384}
Linking options:
https://www.mathnet.ru/eng/timm80
https://www.mathnet.ru/eng/timm/v13/i1/p166
This publication is cited in the following 14 articles:
A. S. Vasilev, “Normalizatory silovskikh podgrupp v simplekticheskikh i ortogonalnykh gruppakh nad konechnymi polyami nechetnoi kharakteristiki”, Tr. IMM UrO RAN, 30, no. 1, 2024, 61–69
Wenbin Guo, Danila O. Revin, Evgeny P. Vdovin, “The reduction theorem for relatively maximal subgroups”, Bull. Math. Sci., 12:01 (2022)
N. Yang, A. A. Galt, “On the local case in the Aschbacher theorem for symplectic and orthogonal groups”, Siberian Math. J., 62:2 (2021), 377–382
A. S. Vasil'ev, “Normalizers of Sylow subgroups in finite linear and
unitary groups”, Algebra and Logic, 59:1 (2020), 1–17
A. A. Galt, D. O. Revin, “Lokalnyi sluchai v teoreme Ashbakhera dlya lineinykh i unitarnykh grupp”, Sib. elektron. matem. izv., 13 (2016), 1207–1218
Wenbin Guo, D.O. Revin, E.P. Vdovin, “Confirmation for Wielandt's conjecture”, Journal of Algebra, 434 (2015), 193
A. A. Galt, W. Guo, E. M. Averkin, D. O. Revin, “On the local case in the Aschbacher theorem for linear and unitary groups”, Siberian Math. J., 55:2 (2014), 239–245
D. O. Revin, “On Baer–Suzuki $\pi$-theorems”, Siberian Math. J., 52:2 (2011), 340–347
E. P. Vdovin, D. O. Revin, “Theorems of Sylow type”, Russian Math. Surveys, 66:5 (2011), 829–870
D. O. Revin, “On a relation between the Sylow and Baer–Suzuki theorems”, Siberian Math. J., 52:5 (2011), 904–913
Revin D.O., Vdovin E.P., “On the number of classes of conjugate Hall subgroups in finite simple groups”, J. Algebra, 324:12 (2010), 3614–3652
D. O. Revin, “Vokrug gipotezy F. Kholla”, Sib. elektron. matem. izv., 6 (2009), 366–380
D. O. Revin, “The $D_\pi$-property in finite simple groups”, Algebra and Logic, 47:3 (2008), 210–227
D. O. Revin, “The $D_\pi$-property of linear and unitary groups”, Siberian Math. J., 49:2 (2008), 353–361
Citation in format AMSBIB
Contact us: