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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 4, Pages 773–790
DOI: https://doi.org/10.17377/smzh.2018.59.404 (Mi smj3009) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On the pronormality of subgroups of odd index in some extensions of finite groups

W. Guoa, N. V. Maslovabc, D. O. Revindea

a University of Science and Technology of China, Hefei, P. R. China
b Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia
c Ural Federal University, Ekaterinburg, Russia
d Sobolev Institute of Mathematics, Novosibirsk, Russia
e Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (364 kB) Citations (10)
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DOI: https://doi.org/10.17377/smzh.2018.59.404
Abstract: We study finite groups with the following property $(*)$: All subgroups of odd index are pronormal. Suppose that $G$ has a normal subgroup $A$ with property $(*)$, and the Sylow $2$-subgroups of $G/A$ are self-normalizing. We prove that $G$ has property $(*)$ if and only if so does $N_G(T)/T$, where $T$ is a Sylow $2$-subgroup of $A$. This leads to a few results that can be used for the classification of finite simple groups with property $(*)$.
Keywords: finite group, pronormal subgroup, Sylow $2$-subgroup, subgroup of odd index, wreath product, direct product, self-normalizing subgroup, simple group, symplectic group.
Funding agency Grant number
National Natural Science Foundation of China 11771409
Ministry of Education and Science of the Russian Federation МК-6118.2016.1
02.A03.21.0006
CAS President's International Fellowship Initiative 2016VMA078
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.1.1, 0314-2016-0001
The first author was supported by the NNSF of China (Grant 11771409). The second author was supported by the President of the Russian Federation (Grant MK-6118.2016.1) and the State Maintenance Program for the Leading Universities of the Russian Federation (Agreement 02.A03.21.0006 of 27.08.2013). The third author was supported by the CAS President's International Fellowship Initiative (Grant 2016VMA078) and the Program of Fundamental Scientific Research of the Siberian Branch of the Russian Academy of Sciences No. I.1.1 (Project 0314- 2016-0001).
Received: 11.10.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 4, Pages 610–622
DOI: https://doi.org/10.1134/S0037446618040043
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: W. Guo, N. V. Maslova, D. O. Revin, “On the pronormality of subgroups of odd index in some extensions of finite groups”, Sibirsk. Mat. Zh., 59:4 (2018), 773–790; Siberian Math. J., 59:4 (2018), 610–622
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
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