Тип публикации: статья из журнала

Год издания: 2014

Идентификатор DOI: 10.1134/S0081543814090119

Ключевые слова: composition factor, finite group, maximal subgroup, minimal group, prime spectrum

Аннотация: Suppose that L is a finite group, ?(L) is the set of prime divisors of the order |L|, and (Formula presented.) is the class of finite groups G such that ?(G) ? ?(H) for any proper subgroup H of G. Groups from the class (Formula presented.) will be called prime spectrum minimal. Many but not all finite simple groups are prime spectrПоказать полностьюum minimal. For finite simple groups not from the class (Formula presented.), the question whether they are isomorphic to nonabelian composition factors of groups from the class (Formula presented.) is interesting. We describe some finite simple groups that are not isomorphic to nonabelian composition factors of groups from the class (Formula presented.) and construct an example of a finite group from (Formula presented.) that has as its composition factor the finite simple sporadic McLaughlin group McL not from the class (Formula presented.). © 2014, Pleiades Publishing, Ltd.

Журнал: Proceedings of the Steklov Institute of Mathematics

Выпуск журнала: Vol. 287, Is. 1

Номера страниц: 116-127

• Maslova N.V. (Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, Russian Federation, Graduate School of Economics and Management, Ural Federal University, ul. Mira 19, Yekaterinbu)
• Revin D.O. (Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, Russian Federation, Novosibirsk State University, ul. Pirogova 2, Novosibirsk, Russian Federation)

• Scopus