Free centre-by-(abelian-by-exponent 2) groups

JOURNAL OF ALGEBRA

卷:430

Article

Alexandrou, Maria¹  Stoehr, Ralph¹ 

[1] Univ Manchester, Dept Math, Manchester M13 9PL, Lancs, England

关键词: Free centre-by-metabelian groups;    Homology of groups;   

DOI  :  10.1016/j.jalgebra.2015.02.014

来源: Elsevier

【 摘 要 】

We study free centre-by-(abelian-by-exponent 2) groups. Our main result is a complete description of the centre. It is isomorphic to a direct sum of a free abelian group and a torsion subgroup. The latter is a direct sum of cyclic groups of order two and cyclic groups of order four. We exhibit a generating set consisting of elements of infinite order, order 2, and order 4, such that the centre is the direct sum of cyclic subgroups generated by those generators. Our approach makes essential use of homological methods. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free