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Title: | Criterions of supersolubility of some finite factorizable grou |
Authors: | Legchekova, Helena V. |
Keywords: | алгебра |
Issue Date: | 2005 |
Publisher: | ДЗ "Луганський національний університет імені Тараса Шевченка |
Abstract: | Let A, B be subgroups of a group G and ∅ 6= X ⊆ G. A subgroup A is said to be X-permutable with B if for some x ∈ X we have ABx = BxA. We obtain some new criterions for supersolubility of a finite group G = AB, where A and B are supersoluble groups. In particular, we prove that a finite group G = AB is supersoluble provided A, B are supersolube subgroups of G such that every primary cyclic subgroup of A X-permutes with every Sylow subgroup of B and if in return every primary cyclic subgroup of B X-permutes with every Sylow subgroup of A where X = F(G) is the Fitting subgroup of G. |
Description: | Criterions of supersolubility of some finite factorizable groups / Helena V. Legchekova // Algebra and Discrete Mathematics. - 2005. - № 3. - 46-55. |
URI: | http://hdl.handle.net/123456789/422 |
ISSN: | 1726-3255 |
Appears in Collections: | Статті |
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