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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2019 Volume 60, Number 2, Pages 429–440 (Mi smj3086)

This article is cited in 5 papers

Groups with prescribed systems of Schmidt subgroups

V. I. Murashka

Francisk Skorina Gomel State University, Gomel, Belarus

Abstract: A Schmidt $(p, q)$-group is a Schmidt group $G$ with $\pi(G) = \{p, q\}$ and normal Sylow $p$-subgroup. The $N$-critical graph $\Gamma_{Nc}(G)$ of a group $G$ is the directed graph with the vertex set $\pi(G)$ in which $(p, q)$ is an edge iff $G$ has a Schmidt $(p, q)$-subgroup. The finite groups for which the degrees of vertices of the $N$-critical graph are at most $2$ are studied.

Keywords: finite group, Schmidt group, directed graph, $N$-critical graph, Sylow graph, Hawkes graph, formation with the Shemetkov property.

UDC: 512.542

MSC: 35R30

Received: 28.05.2018
Revised: 11.09.2018
Accepted: 17.10.2018

DOI: 10.33048/smzh.2019.60.214


 English version:
Siberian Mathematical Journal, 2019, 60:2, 334–342

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© Steklov Math. Inst. of RAS, 2025