Тип публикации: статья из журнала

Год издания: 2014

Идентификатор DOI: 10.1134/S0081543814050150

Ключевые слова: finite group, generation by a pair of conjugate elements, Hall subgroup, maximal subgroup, prime spectrum

Аннотация: For a finite group G, the set of all prime divisors of {pipe}G{pipe} is denoted by ?(G). P. Shumyatsky introduced the following conjecture, which was included in the "Kourovka Notebook" as Question 17.125: a finite group G always contains a pair of conjugate elements a and b such that ?(G) = ?(?a, b?). Denote by (Formula presented)Показать полностьюthe class of all finite groups G such that ?(H) ? ?(G) for every maximal subgroup H in G. Shumyatsky's conjecture is equivalent to the following conjecture: every group from (Formula presented) is generated by two conjugate elements. Let (Formula presented) be the class of all finite groups in which every maximal subgroup is a Hall subgroup. It is clear that (Formula presented). We prove that every group from (Formula presented) is generated by two conjugate elements. Thus, Shumyatsky's conjecture is partially supported. In addition, we study some properties of a smallest order counterexample to Shumyatsky's conjecture. © 2014 Pleiades Publishing, Ltd.

Журнал: Proceedings of the Steklov Institute of Mathematics

Выпуск журнала: Vol. 285, Is. SUPPL.1

Номера страниц: 139-145

• Maslova N.V. (Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russian Federation, Graduate School of Economics and Management, Ural Federal University, ul. Mira 19, Yek)
• Revin D.O. (Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation, Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russian Federation)

• Scopus