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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 2, Pages 430–440 (Mi smj2208)  
This article is cited in 12 scientific papers (total in 12 papers)

On Baer–Suzuki $\pi$-theorems

D. O. Revinab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk, Russia
Full-text PDF (340 kB) Citations (12)
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Abstract: Given a set $\pi$ of primes, say that the Baer–Suzuki $\pi$-theorem holds for a finite group $G$ if only an element of $\mathscr O_\pi(G)$ can, together with each conjugate element, generate a $\pi$-subgroup. We find a sufficient condition for the Baer–Suzuki $\pi$-theorem to hold for a finite group in terms of nonabelian composition factors. We show also that in case $2\not\in\pi$ the Baer–Suzuki $\pi$-theorem holds for every finite group.
Keywords: finite simple group, Baer–Suzuki theorem, $\pi$-element, $\pi$-subgroup, $\pi$-radical, Sylow theorem, Hall $\pi$-subgroup, property $D_\pi$.
Received: 02.06.2010
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 2, Pages 340–347
DOI: https://doi.org/10.1134/S0037446611020170
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: D. O. Revin, “On Baer–Suzuki $\pi$-theorems”, Sibirsk. Mat. Zh., 52:2 (2011), 430–440; Siberian Math. J., 52:2 (2011), 340–347
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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