The weak minimal condition on subgroups which fail to be close to normal subgroups

JOURNAL OF ALGEBRA

卷:560

Article

Dardano, Ulderico¹  De Mari, Fausto¹  Rinauro, Silvana¹ 

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia Monte S Angelo, I-80126 Naples, Italy

关键词: Nearly normal;    Almost normal;    Core-finite;    Minimax;    Finite rank;   

DOI  :  10.1016/j.jalgebra.2020.04.034

来源: Elsevier

【 摘 要 】

A subgroup H of a group G is commensurable (or close) to a normal subgroup if there is a normal subgroup N of G such that the index vertical bar HN : (H boolean AND N)vertical bar is finite; if further the subgroup N can be chosen to be contained in H, i.e. if H/H-G is finite, then H is called core-finite. We describe the structure of (generalized) soluble groups satisfying the weak minimal condition on subgroups that are not commensurable with a normal subgroup. Our results describe also (generalized) soluble groups satisfying the weak minimal condition on non-(core-finite) subgroups. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free