On permuteral subgroups in finite groups

The permutizer of a subgroup H in a group G is defined as the subgroup generated by all cyclic subgroups of G that permute with H . Call H permuteral in G if the permutizer of H in G coincides with G ; H is called strongly permuteral in G if the permutizer of H in U coincides with U for every subgro...

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Bibliographic Details
Published inSiberian mathematical journal Vol. 55; no. 2; pp. 230 - 238
Main Authors Vasil’ev, A. F., Vasil’ev, V. A., Vasil’eva, T. I.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2014
Subjects
Mathematics
Mathematics and Statistics
w-supersoluble group
supersoluble group
finite group
permuteral subgroup
permutizer of a subgroup
ℙ-subnormal subgroup
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Summary:The permutizer of a subgroup H in a group G is defined as the subgroup generated by all cyclic subgroups of G that permute with H . Call H permuteral in G if the permutizer of H in G coincides with G ; H is called strongly permuteral in G if the permutizer of H in U coincides with U for every subgroup U of G containing H . We study the finite groups with given systems of permuteral and strongly permuteral subgroups and find some new characterizations of w-supersoluble and supersoluble groups.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446614020050