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Some properties of endomorphisms in residually finite groups

Published online by Cambridge University Press:  09 April 2009

Ronald Hirshon
Ronald Hirshon
Affiliation:
Department of Mathematics, Polytechnic Institute of New York, Brooklyn, New York, U.S.A.
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Abstract

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If ε is an endomorphism of a finitely generated residually finite group onto a subgroup Fε of finite index in F, then there exists a positive integer k such that ε is an isomorphism of Fεk. If K is the kernel of ε, then K is a finite group so that if F is a non trivial free product or if F is torsion free, then ε is an isomorphism on F. If ε is an endomorphism of a finitely generated resedually finite group onto a subgroup Fε (not necessatily of ginite index in F) and if the kernel of ε obeys the minimal condition for subgroups then there exists a positive integer k such that ε is an isomorphism on Fεk.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1977 , pp. 117 - 120
Copyright
Copyright © Australian Mathematical Society 1977

References

Kurosh, A. G. (1956), The Theory of Groups, Vol. 2 (translated by Hirsch, K. from the second Russian edition). Chelsea, New York.Google Scholar
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Magnus, W. (1969), ‘Residually finite groups’, Bull. Amer. Math Soc. 75, 305–316.CrossRefGoogle Scholar