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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2013, Volume 10, Pages 436–442 (Mi semr423)  
Mathematical logic, algebra and number theory

On the commutation graph of cyclic $TI$-subgroup in a symmetric group

N. D. Zyulyarkina

South Ural State University, Chelyabinsk
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Abstract: We study the commutation graph $\Gamma _G(A)$ of cyclic $TI$-subgroup A of order 4 in a finite group $G$ with quasisimple generalized Fitting subgroup $F^*(G)$. It is proved that, if $F^*(G)$ is a covering group for $A_n$, then the graph $\Gamma _G(A)$ is edge-regular but not coedge-regular graph.
Keywords: finite group, cyclic $TI$-subgroup, commutation graph.
Received May 1, 2013, published May 22, 2013
Document Type: Article
UDC: 519.17+512.54
MSC: 05C25
Language: Russian
Citation: N. D. Zyulyarkina, “On the commutation graph of cyclic $TI$-subgroup in a symmetric group”, Sib. Èlektron. Mat. Izv., 10 (2013), 436–442
Citation in format AMSBIB
\Bibitem{Zyu13}
\by N.~D.~Zyulyarkina
\paper On the commutation graph of cyclic $TI$-subgroup in a symmetric group
\jour Sib. \`Elektron. Mat. Izv.
\yr 2013
\vol 10
\pages 436--442
\mathnet{http://mi.mathnet.ru/semr423}
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