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.
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