On finite simple classical groups over fields of different characteristics with coinciding prime graphs


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Аннотация

Suppose that G is a finite group, π(G) is the set of prime divisors of its order, and ω(G) is the set of orders of its elements. We define a graph on π(G) with the following adjacency relation: different vertices r and s from π(G) are adjacent if and only if rsω(G). This graph is called the Gruenberg–Kegel graph or the prime graph of G and is denoted by GK(G). Let G and G1 be two nonisomorphic finite simple groups of Lie type over fields of orders q and q1, respectively, with different characteristics. It is proved that, if G is a classical group of a sufficiently high Lie rank, then the prime graphs of the groups G and G1 may coincide only in one of three cases. It is also proved that, if G = A1(q) and G1 is a classical group, then the prime graphs of the groups G and G1 coincide only if {G, G1} is equal to {A1(9), A1(4)}, {A1(9), A1(5)}, {A1(7), A1(8)}, or {A1(49),2A3(3)}.

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Авторлар туралы

M. Zinov’eva

Krasovskii Institute of Mathematics and Mechanics; Ural Federal University

Хат алмасуға жауапты Автор.
Email: zinovieva-mr@yandex.ru
Ресей, Yekaterinburg, 620990; Yekaterinburg, 620000

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