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A class of groups rich in finite quotients

Published online by Cambridge University Press:  18 May 2009

Vonn Walter
Vonn Walter
Affiliation:
Department of Mathematics, Southeastern Oklahoma State University, Durant, OK, 74701, USA
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If X is a class of groups, the class of counter-Xgroups is defined to consist of all groups having no non-trivial X-quotients. The counter-abelian groups are the perfect groups and the counter-counter-abelian groups are the imperfect groups studied by Berrick and Robinson [2]. This paper is concerned with the class of counter-counterfinite groups. It turns out that these are the groups in which any non-trivial quotient has a non-trivial representation over any finitely generated domain (Theorem 1.1), so we shall call these groups highly representable or HR-groups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 3 , September 1996 , pp. 263 - 274
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

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