Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
On the existence of complements in a group to some abelian normal subgroups
Репозиторій DSpace/Manakin
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On the existence of complements in a group to some abelian normal subgroups
Інший ID:
2010 Mathematics Subject Classification:20E22, 20E26, 20F50
Посилання:
On the existence of complements in a group to some abelian normal subgroups / M.R. Dixon, L.A. Kurdachenko, Javier Otal // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 18–41. — Бібліогр.: 32 назв. — англ.
Підтримка:
The second and third authors were supported by Proyecto MTM2010-19938-C03-03of Direcci ́on General de Investigaci ́on del MICINN (Spain)
Дата:
2010
Переглядів:
453
Завантажень:
181
Анотація:
A complement to a proper normal subgroup H of a group G is a subgroup K such that G=HK and H∩K=⟨1⟩. Equivalently it is said that G splits over H. In this paper we develop a theory that we call hierarchy of centralizers to obtain sufficient conditions for a group to split over a certain abelian subgroup. We apply these results to obtain an entire group-theoretical wide extension of an important result due to D. J. S. Robinson formerly shown by cohomological methods.
