Finitely Solvable Groups with Nilpotent Wide Subgroups

A subgroup H of a finite group G is called wide if each prime divisor of the order of G divides the order of H. We obtain a description of finite solvable groups without wide subgroups. It is shown that a finite solvable group with nilpotent wide subgroups contains a quotient group with respect to t...

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Veröffentlicht in:	Ukrainian mathematical journal 2016-12, Vol.68 (7), p.1091-1096
Hauptverfasser:	Monakhov, V. S., Sokhor, I. L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Statistics Subgroups
Online-Zugang:	Volltext
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Zusammenfassung:	A subgroup H of a finite group G is called wide if each prime divisor of the order of G divides the order of H. We obtain a description of finite solvable groups without wide subgroups. It is shown that a finite solvable group with nilpotent wide subgroups contains a quotient group with respect to the hypercenter without wide subgroups.
ISSN:	0041-5995 1573-9376
DOI:	10.1007/s11253-016-1279-1