FREE CENTRE-BY-(ABELIAN-BY-EXPONENT 2) GROUPS

Alexandrou, Maria and Stöhr, Ralph (2013) FREE CENTRE-BY-(ABELIAN-BY-EXPONENT 2) GROUPS. [MIMS Preprint]

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Abstract

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 innite 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.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Prof Ralph Stöhr
Date Deposited:	26 Nov 2013
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2072

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