On permuteral subgroups in finite groups |
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Authors: | A F Vasil’ev V A Vasil’ev T I Vasil’eva |
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Institution: | 1. Francisk Skorina Gomel State University, Gomel, Belarus 2. Belarusian State University of Transport, Gomel, Belarus
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Abstract: | 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. |
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