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Hopfian and co-Hopfian groups

Published online by Cambridge University Press:  17 April 2009

Satya Deo  and
K. Varadarajan
Satya Deo
Affiliation:
Department of MathematicsR.D. UniversityJabalpur 482001India
K. Varadarajan
Affiliation:
Department of MathematicsUniversity of CalgaryCalgary, AlbertaCanada T2N 1N4
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Abstract

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The main results proved in this note are the following:

(i) Any finitely generated group can be expressed as a quotient of a finitely presented, centreless group which is simultaneously Hopfian and co-Hopfian.

(ii) There is no functorial imbedding of groups (respectively finitely generated groups) into Hopfian groups.

(iii) We prove a result which implies in particular that if the double orientable cover N of a closed non-orientable aspherical manifold M has a co-Hopfian fundamental group then π1(M) itself is co-Hopfian.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 17 - 24
Copyright
Copyright © Australian Mathematical Society 1997

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