Classification and properties of the π -submaximal subgroups in minimal nonsolvable groups

Wenbin Guo, Danila O. Revin

Результат исследования: Научные публикации в периодических изданияхстатья

5 Цитирования (Scopus)

Аннотация

Let π be a set of primes. According to H. Wielandt, a subgroup H of a finite group X is called a π-submaximal subgroup if there is a monomorphism ϕ: X→ Y into a finite group Y such that Xϕ is subnormal in Y and Hϕ= K∩ Xϕ for a π-maximal subgroup K of Y. In his talk at the celebrated conference on finite groups in Santa-Cruz (USA) in 1979, Wielandt posed a series of open questions and among them the following problem: to describe the π-submaximal subgroup of the minimal nonsolvable groups and to study properties of such subgroups: the pronormality, the intravariancy, the conjugacy in the automorphism group etc. In the article, for every set π of primes, we obtain a description of the π-submaximal subgroup in minimal nonsolvable groups and investigate their properties, so we give a solution of Wielandt’s problem.

Язык оригиналаанглийский
Страницы (с-по)325-351
Число страниц27
ЖурналBulletin of Mathematical Sciences
Том8
Номер выпуска2
DOI
СостояниеОпубликовано - 1 авг 2018

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