N-critical graph of finite groups
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Published:2021-12-02
Issue:
Volume:
Page:
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ISSN:1793-5571
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Container-title:Asian-European Journal of Mathematics
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language:en
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Short-container-title:Asian-European J. Math.
Affiliation:
1. Faculty of Mathematics and Technologies of Programming, Francisk Skorina Gomel State University, 104 Sovetskaya Street 246019, Gomel, Belarus
Abstract
A Schmidt [Formula: see text]-group is a non-nilpotent [Formula: see text]-group whose proper subgroups are nilpotent and which has the normal Sylow [Formula: see text]-subgroup. The [Formula: see text]-critical graph [Formula: see text] of a finite group [Formula: see text] is a directed graph on the vertex set [Formula: see text] of all prime divisors of [Formula: see text] and [Formula: see text] is an edge of [Formula: see text] if and only if [Formula: see text] has a Schmidt [Formula: see text]-subgroup. The bounds of the nilpotent length of a soluble group are obtained in terms of its [Formula: see text]-critical graph. The structure of a soluble group with given [Formula: see text]-critical graph is obtained in terms of commutators. The connections between [Formula: see text]-critical and other graphs (Sylow, soluble, prime, commuting) of finite groups are found.
Funder
Belarusian Republican Foundation for Fundamental Research
Publisher
World Scientific Pub Co Pte Ltd
Subject
General Mathematics
Cited by
1 articles.
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1. On the Hawkes Graphs of Finite Groups;Siberian Mathematical Journal;2022-09