Primary Cosets in Groups

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование


A finite group G is called a generalized Frobenius group with kernel F if F is a proper nontrivial normal subgroup of G, and for every element Fx of prime order p in the quotient group G/F, the coset Fx of G consists of p-elements. We study generalized Frobenius groups with an insoluble kernel F. It is proved that F has a unique non- Abelian composition factor, and that this factor is isomorphic to L2(32l) for some natural number l. Moreover, we look at a (not necessarily finite) group generated by a coset of some subgroup consisting solely of elements of order three. It is shown that such a group contains a nilpotent normal subgroup of index three.

Язык оригиналаанглийский
Страницы (с-по)216-221
Число страниц6
ЖурналAlgebra and Logic
Номер выпуска3
СостояниеОпубликовано - июл 2020


Подробные сведения о темах исследования «Primary Cosets in Groups». Вместе они формируют уникальный семантический отпечаток (fingerprint).