Involutory decomposition of a group and twisted subsets with few involutions

Описание

Тип публикации: статья из журнала

Год издания: 2008

Идентификатор DOI: 10.1007/s11202-008-0022-z

Ключевые слова: involutory decomposition of a group, twisted subset, twisted subgroup

Аннотация: A subset K of some group C is called twisted if 1 is an element of K and x, y is an element of K implies that xy(-1)x belongs to K. We use the concept of twisted subset to investigate and generalize the concept of involutory decomposition of a group. A group is said to admit involutory decomposition if it contains some involution sПоказать полностьюuch that the group is the product of the centralizer of the involution and the set of elements inverted by the involution. We study the twisted subsets with at most one involution. We prove that if a twisted subset has no involutions at all then it generates a subgroup of odd order.

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Издание

Журнал: SIBERIAN MATHEMATICAL JOURNAL

Выпуск журнала: Vol. 49, Is. 2

Номера страниц: 218-221

ISSN журнала: 00374466

Место издания: NEW YORK

Издатель: CONSULTANTS BUREAU/SPRINGER

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