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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 2, Pages 168–183
(Mi timm1068)
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This article is cited in 3 scientific papers (total in 3 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.
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
Linking options:
https://www.mathnet.ru/eng/timm1068 https://www.mathnet.ru/eng/timm/v20/i2/p168
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Abstract page: | 311 | Full-text PDF : | 75 | References: | 58 | First page: | 5 |
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