Groups of infinite rank with finite conjugacy classes of subnormal subgroups

JOURNAL OF ALGEBRA

卷:431

Article

De Falco, M.¹  de Giovanni, F.¹  Musella, C.¹  Trabelsi, N.² 

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy

[2] Univ Setif 1, Dept Math, Lab Fundamental & Numer Math, Setif 19000, Algeria

关键词: Subnormal subgroup;    Conjugacy class;    Normal closure;    Infinite rank;   

DOI  :  10.1016/j.jalgebra.2015.01.031

来源: Elsevier

【 摘 要 】

A group is called a V-group if it has finite conjugacy classes of subnormal subgroups. It is proved here that if G is a periodic soluble group in which every subnormal subgroup of infinite rank has finitely many conjugates, then G is a V-group, provided that its Hirsch-Plotkin radical has infinite rank. Corresponding results for periodic soluble groups in which every subnormal subgroup of infinite rank has finite index in its normal closure and for those in which every subnormal subgroup of infinite rank is finite over its core, are also obtained. Moreover, it is shown that the assumption on the Hirsch-Plotkin radical can be avoided in the case of periodic groups with nilpotent commutator subgroup. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free