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Some topological properties of residually Černikov groups

Published online by Cambridge University Press:  18 May 2009

M. R. Dixon
M. R. Dixon
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A.
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In this paper we shall indicate how to generalise the concept of a cofinite group (see [7]). We recall that any residually finite group can be made into a topological group by taking as a basis of neighbourhoods of the identity precisely the normal subgroups of finite index. The class of compact cofinite groups is then easily seen to be the class of profinite groups, where a group is profinite if and only if it is an inverse limit of finite groups. It turns out that every cofinite group can be embedded as a dense subgroup of a profinite group. This has important consequences for the class of countable locally finite-soluble groups with finite Sylow p-subgroups for all primes p, as shown in [7] and [14].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 1 , January 1982 , pp. 65 - 82
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

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