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ON GROUPS THAT ARE ISOMORPHIC WITH EVERY SUBGROUP OF FINITE INDEX AND THEIR TOPOLOGY

Published online by Cambridge University Press:  01 February 1998

DEREK J. S. ROBINSON  and
MATHEW TIMM
DEREK J. S. ROBINSON
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA. E-mail: robinson@math.uiuc.edu
MATHEW TIMM
Affiliation:
Department of Mathematics, Bradley University, Peoria, IL 61625, USA. E-mail: mtimm@bradley.bradley.edu
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Abstract

The main result is that a finitely generated group that is isomorphic to all of its finite index subgroups has free Abelian first homology, and that its commutator subgroup is a perfect group. A number of corollaries on the structure of such groups are obtained, including a method of constructing all such groups for which the commutator subgroup has a trivial centralizer. As an application, conditions are presented for the covering spaces of compact manifolds that determine when the fundamental groups of the base spaces are free Abelian.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 91 - 104
Copyright
The London Mathematical Society 1998

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