Тип публикации: статья из журнала

Год издания: 2017

Идентификатор DOI: 10.1134/S0081543817020134

Ключевые слова: complement of a subgroup, finite simple group, pronormal subgroup, subgroup of odd index, supplement of a subgroup

Аннотация: A subgroup H of a group G is called pronormal if, for any element g ∈ G, the subgroups H and Hg are conjugate in the subgroup H,Hg. We prove that, if a group G has a normal abelian subgroup V and a subgroup H such that G = HV, then H is pronormal in G if and only if U = NU(H)[H,U] for any H-invariant subgroup U of V. Using this facПоказать полностьюt, we prove that the simple symplectic group PSp6n(q) with q ≡ ±3 (mod 8) contains a nonpronormal subgroup of odd index. Hence, we disprove the conjecture on the pronormality of subgroups of odd indices in finite simple groups, which was formulated in 2012 by E.P. Vdovin and D.O. Revin and verified by the authors in 2015 for many families of simple finite groups. © 2017, Pleiades Publishing, Ltd.

Журнал: Proceedings of the Steklov Institute of Mathematics

Выпуск журнала: Vol. 296

Номера страниц: 145-150

ISSN журнала: 00815438

Издатель: Maik Nauka-Interperiodica Publishing

• Kondrat’ev A.S. (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation, Ural Federal University, Yekaterinburg, Russian Federation)
• Maslova N.V. (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation, Ural Federal University, Yekaterinburg, Russian Federation)
• Revin D.O. (Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation, Novosibirsk State University, Novosibirsk, Russian Federation)

• Scopus