N.A. Minigulov. Finite almost simple 4-primary groups with connected Gruenberg–Kegel graph ... P.142-146

Let $G$ be a finite group. Denote by $\pi(G)$ the set of prime divisors of the order of $G$. The Gruenberg-Kegel graph (prime graph) of $G$ is the graph with the vertex set $\pi(G)$ in which two different vertices $p$ and $q$ are adjacent if and only if $G$ has an element of order $pq$. If $|\pi(G)|=n$, then the group $G$ is called $n$-primary. In 2011, A.S. Kondrat'ev and I.V. Khramtsov described finite almost simple 4-primary groups with disconnected Gruenberg-Kegel graph. In the present paper we describe finite almost simple 4-primary groups with connected Gruenberg-Kegel graph. For each of these groups, its Gruenberg-Kegel graph is found. The results are presented in a table. According to the table, there are 32 such groups. The results are obtained with the use of the computer system GAP.

Keywords: finite group, almost simple group, 4-primary group, Gruenberg-Kegel graph

Received August 12, 2019

Revised September 15, 2019

Accepted September 23, 2019

Funding Agency: This work was supported by the Russian Science Foundation (project no. 19-71-10067).

Nikolai Aleksandrovich Minigulov, doctoral student, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: nikola-minigulov@mail.ru

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Cite this article as: N.A.Minigulov. Finite almost simple 4-primary groups with connected Gruenberg–Kegel graph, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 4, pp. 142–146.