On rationality and 2-reflexiveness of wreath products of finite groups

Описание

Тип публикации: статья из журнала

Год издания: 2006

Идентификатор DOI: 10.1007/s11006-006-0150-3

Ключевые слова: wreath product; Sylow group; rational group; 2-reflexive group; irreducible character; classical linear group; dihedral group

Аннотация: A finite group G is said to be rational if each its irreducible character acquires only rational values, and it is said to be 2-reflexive if each its element can be represented as a product of at most two involutions. We find necessary and sufficient conditions for the wreath of two finite groups be rational and 2-reflexive. NamelyПоказать полностью, we show that the wreath H integral K of two finite groups H and K is a rational (respectively, 2-reflexive) group iff H is a rational (respectively, 2-reflexive) group and K is an elementary Abelian 2-group. As a corollary, we obtain a description of all classical linear groups over finite fields of odd characteristic with rational and 2-reflexive Sylow 2-subgroups.

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Издание

Журнал: MATHEMATICAL NOTES

Выпуск журнала: Vol. 80, Is. 3-4

Номера страниц: 380-386

ISSN журнала: 00014346

Место издания: NEW YORK

Издатель: CONSULTANTS BUREAU/SPRINGER

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