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Epimorphisms preserving perfect radicals

Part of: Connections with homological algebra and category theory Categories and geometry Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

A. J. Berrick
A. J. Berrick
Affiliation:
Department of Mathematics, National University of SingaporeKent Ridge Singapore, 0511
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Abstract

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This is an investigation of whether a group epimorphism maps the maximal perfect subgroup of its domain onto that of its image. It is shown how the question arises naturally from considerations of algebraic K-theory and Quillen's plus-construction. Some sufficient conditions are obtained; these relate to the upper central series, or alternatively the derived series, of the domain. By means of topological/homological techniques, the results are then sharpened to provide, in certain circumstances, conditions which are necessary as well as sufficient.

MSC classification

Secondary: 20F14: Derived series, central series, and generalizations 20J05: Homological methods in group theory 18F25: Algebraic $K$-theory and $L$-theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 3 , June 1984 , pp. 357 - 364
Copyright
Copyright © Australian Mathematical Society 1984

References

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