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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 2, Pages 168–183 (Mi timm1068)  

This article is cited in 2 scientific papers (total in 2 papers)

Finite simple groups of Lie type over a field of the same characteristic with the same prime graph

M. R. Zinov'evaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b B. N. Yeltsin Ural Federal University

Abstract: For a finite group $G$, let $\pi(G)$ be the set of prime divisors of its order, and let $\omega(G)$ be the set of orders of its elements. Define on $\pi(G)$ a graph with the following adjacency relation: distinct vertices $r$ and $s$ from $\pi(G)$ are adjacent if and only if $rs\in\omega(G)$. This graph is called the Grunberg–Kegel graph or prime graph of the group $G$ and is denoted by $GK(G)$. We prove that, if $G$ and $G_1$ are nonisomorphic finite simple groups of Lie type over fields of orders $q$ and $q_1$, respectively, of the same characteristic, then the graphs $GK(G)$ and $GK(G_1)$ coincide if and only if either $\{G,G_1\}=\{A_1(8),A_2(2)\}$ or $q=q_1$ and the pair $\{G,G_1\}$ coincides with one of the pairs $\{B_n(q),C_n(q)\}$ for odd $q$, $\{B_3(q),D_4(q)\}$, and $\{C_3(q),D_4(q)\}$.

Keywords: finite simple group of Lie type, prime graph, spectrum.

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Bibliographic databases:

Document Type: Article
UDC: 512.542
Received: 29.10.2013

Citation: M. R. Zinov'eva, “Finite simple groups of Lie type over a field of the same characteristic with the same prime graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 2, 2014, 168–183

Citation in format AMSBIB
\Bibitem{Zin14}
\by M.~R.~Zinov'eva
\paper Finite simple groups of Lie type over a~field of the same characteristic with the same prime graph
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 2
\pages 168--183
\mathnet{http://mi.mathnet.ru/timm1068}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3364149}
\elib{http://elibrary.ru/item.asp?id=21585634}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. R. Zinov'eva, “On finite simple classical groups over fields of different characteristics with coinciding prime graphs”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 223–239  mathnet  crossref  crossref  mathscinet  isi  elib
    2. M. R. Zinoveva, “O konechnykh prostykh lineinykh i unitarnykh gruppakh nad polyami raznykh kharakteristik, grafy prostykh chisel kotorykh sovpadayut. I”, Tr. IMM UrO RAN, 23, no. 4, 2017, 136–151  mathnet  crossref  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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