| Summary: | In the present thesis we study free centre-by-(abelian-by-exponent 2) groups. These are in the class of free centre-by-metabelian groups which in turn are a special case of quotients of the form F=[R0; F] where F is a free group, R is a normal subgroup of F and R0 is the commutator subgroup of R. The latter have been an object of investigation for more than forty years, due to their intriguing feature of having non-trivial torsion under certain conditions. This was first discovered for the case where R = F0. For arbitrary F and R, if there is torsion in F=[R0; F], it is bound to be contained in the central subgroup R0=[R0; F] which decomposes into a direct sum of a free abelian group and a (possibly trivial) torsion group of exponent dividing 4. If F=R has no elements of order 2, then the torsion subgroup is isomorphic to the homology group H4(F=R;Z2). Thus the question that remains open is what happens if F=R contains elements of order 2.
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