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Some Properties on Isologism of Groups

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Mohammad Reza R. Moghaddam  and
Ali Reza Salemkar
Ali Reza Salemkar
Affiliation:
Faculty of Mathematical Sciences Ferdowsi University of MashhadIran e-mail: Moghdam@science2.um.ac.ir
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Abstract

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In this paper a necessary and sufficient condition will be given for groups to be ν-isologic, with respect to a given variety of groups ν. Its is also shown that every ν-isologism family of a group contains a ν-Hopfian group. Finally we show that if G is in the variety ν, then every ν-covering group of G is a Hopfian group.

Keywords

covering groupisologismHopfian group

MSC classification

Secondary: 20E10: Quasivarieties and varieties of groups 20E36: Automorphisms of infinite groups 20F28: Automorphism groups of groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 1 , February 2000 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 2000

References

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