Abstract
Let F be a free group of rank Consider the quotient
the free centre-by-(nilpotent of class 3)-by-abelian group within the variety of all soluble groups of derived length 3. A peculiar feature of this group is the occurence of torsion in its centre. Our main result is a description of an elementary abelian 2-group of rank
in
in terms of generators of F for
Our approach makes essential use of homological methods.
Acknowledgments
The author would like to thank the anonymous referee for helpful comments and suggestions that improved the presentation of the paper.