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Some Properties on Isologism of Groups

Part of: Special aspects of infinite or finite groups Structure and classification 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: [email protected]
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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

[1]Hall, P., ‘The classification of prime-power groups’, J. Reine Angew. Math. 182 (1940), 130–141.CrossRefGoogle Scholar
[2]Hekster, N. S., ‘On the structure of n-isolinism classes of groups’, J. Pure Appl. Algebra 40 (1986), 63–85.CrossRefGoogle Scholar
[3]Hekster, N. S., ‘Varieties of groups and isologisms’, J. Austral. Math. Soc. (Series A) 46 (1989), 22–60.CrossRefGoogle Scholar
[4]Moghaddam, M. R. R., ‘On the Schur-Baer property’, J. Austral. Math. Soc. (Series A) 31 (1981), 343–361.CrossRefGoogle Scholar
[5]Moghaddam, M. R. R. and Salemkar, A. R., ‘Varietal isologisms and covering groups’, Arch. Math., to appear.Google Scholar
[6]Moghaddam, M. R. R., ‘Characterization of varietal covering and stem groups’ Comm. Algebra, to appear.Google Scholar
[7]Moghaddam, M. R. R., Salemkar, A. R. and Nasrabadi, M. M., ‘Some inequalities for the Baerinvariants, and covering groups’, preprint.Google Scholar
[8]Neumann, H., Varieties of groups (Springer, Berlin, 1967).CrossRefGoogle Scholar
[9]Weichsel, P. M., ‘On isoclinism’, J. London Math. Soc. 38 (1963), 63–65.CrossRefGoogle Scholar