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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 1, Pages 165–173
DOI: https://doi.org/10.17377/smzh.2017.58.116 (Mi smj2849) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On pronormality and strong pronormality of Hall subgroups

M. N. Nesterovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (297 kB) Citations (4)
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DOI: https://doi.org/10.17377/smzh.2017.58.116
Abstract: We study several well-known questions on pronormality and strong pronormality of Hall subgroups. In particular, we exhibit the examples of finite groups (a) having a Hall subgroup not pronormal in its normal closure (this solves Problem 18.32 of The Kourovka Notebook in the negative); (b) having a Hall subgroup pronormal but not strongly pronormal; and (c) that are simple, having a Hall subgroup, and not strongly pronormal (this solves Problem 17.45(b) of The Kourovka Notebook in the negative).
Keywords: Hall subgroup, pronormal subgroup, strongly pronormal subgroup, finite simple group.
Funding agency Grant number
Russian Science Foundation 14-21-00065
The author was supported by the Russian Science Foundation (Grant 14-21-00065).
Received: 03.03.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 1, Pages 128–133
DOI: https://doi.org/10.1134/S0037446617010165
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 35R30
Language: Russian
Citation: M. N. Nesterov, “On pronormality and strong pronormality of Hall subgroups”, Sibirsk. Mat. Zh., 58:1 (2017), 165–173; Siberian Math. J., 58:1 (2017), 128–133
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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