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Sbornik: Mathematics, 2013, Volume 204, Issue 12, Pages 1839–1848
DOI: https://doi.org/10.1070/SM2013v204n12ABEH004363 (Mi sm8182) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On Isaacs' problem

A. A. Yadchenko

Institute of Mathematics of the National Academy of Sciences of Belarus
English version PDF (434 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2013v204n12ABEH004363
Abstract: Let $G$ be a $\pi$-soluble irreducible complex linear group of degree $n$ such that a Hall $\pi$-subgroup $H$ of it has odd order, is a $\mathrm{TI}$-subgroup, and is not normal in $G$. In this paper it is established that $n$ is divisible by $|H|$ or by a power $f>1$ of some prime number such that $f\equiv \pm 1\ (\operatorname{mod}|H|)$.
Bibliography: 15 titles.
Keywords: groups, character degrees, normal subgroups.
Received: 10.10.2012 and 28.06.2013
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 12, Pages 147–156
DOI: https://doi.org/10.4213/sm8182
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: Primary 20C15; Secondary 20D60
Language: English
Original paper language: Russian
Citation: A. A. Yadchenko, “On Isaacs' problem”, Mat. Sb., 204:12 (2013), 147–156; Sb. Math., 204:12 (2013), 1839–1848
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v204/i12/p147
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:359
    Russian version PDF:146
    English version PDF:5
    References:41
    First page:39
     
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