Groups in which each subgroup is commensurable with a normal subgroup

JOURNAL OF ALGEBRA

卷:496

Article

Casolo, Carlo¹  Dardano, Ulderico²  Rinauro, Silvana³ 

[1] Univ Florence, Dipartimento Matemat U Dini, Viale Morgagni 67A, I-50134 Florence, Italy

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

[3] Univ Basilicata, Dipartimento Matemat Informat & Econ, Via Ateneo Lucano 10 Contrada Macchia Romana, I-85100 Potenza, Italy

关键词: Locally finite;    Core-finite;    Subnormal;    Nilpotent;   

DOI  :  10.1016/j.jalgebra.2017.11.016

来源: Elsevier

【 摘 要 】

A group G is a CN-group if for each subgroup H of G there exists a normal subgroup N of G such that the index vertical bar HN : (H boolean AND N)vertical bar is finite. The class of cN-groups contains properly the classes of core-finite groups and that of groups in which each subgroup has finite index in a normal subgroup. In the present paper it is shown that a CN-group whose periodic images are locally finite is finite-by-abelian-by-finite. Such groups are then described into some details by considering automorphisms of abelian groups. Finally, it is shown that if G is a locally graded group with the property that the above index is bounded independently of H, then G is finite-by-abelian-by-finite. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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