Groups with few conjugacy classes of non-normal subgroups

Mathematica Slovaca

Maria Falco¹  Francesco Giovanni¹  Carmela Musella¹ 

关键词: conjugacy class;    metahamiltonian group;   

DOI  :  10.2478/s12175-008-0066-3

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

The structure of groups with finitely many non-normal subgroups is well known. In this paper, groups are investigated with finitely many conjugacy classes of non-normal subgroups with a given property. In particular, it is proved that a locally soluble group with finitely many non-trivial conjugacy classes of non-abelian subgroups has finite commutator subgroup. This result generalizes a theorem by Romalis and Sesekin on groups in which every non-abelian subgroup is normal.

【 授权许可】

Unknown