Тип публикации: статья из журнала
Год издания: 2013
Идентификатор DOI: 10.1007/s10469-013-9254-5
Ключевые слова: finite group, Glauberman's Z*-theorem
Аннотация: Glauberman's Z (*)-theorem [1] and the theorem of Bender are two most important tools for local analysis in the theory of finite groups. The Z (*)-theorem generalizes the known Burnside and Brauer-Suzuki theorems on finite groups with cyclic and quaternion Sylow 2-subgroups. Whether these theorems are valid in a class of periodic gПоказать полностьюroups is unknown. We prove that the Z (*)-theorem is invalid in the class of all periodic groups. In particular, this gives negative answers to questions of A. V. Borovik [3, Question 11.13] and V. D. Mazurov [3, Question 17.71a].
Журнал: ALGEBRA AND LOGIC
Выпуск журнала: Vol. 52, Is. 5
Номера страниц: 422-425
ISSN журнала: 00025232
Место издания: NEW YORK
Издатель: SPRINGER