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On the co-Dedekindian finite p-groups with non-cyclic abelian second centre

Published online by Cambridge University Press:  18 July 2002

Ali-Reza Jamali  and
Hamid Mousavi
Ali-Reza Jamali
Affiliation:
Institute of Mathematics, University for Teacher Education, Tehran 15614, Iran e-mail: jamali@saba.tmu.ac.ir
Hamid Mousavi
Affiliation:
Institute for Studies in Theoretical Physics and Mathematics, University for Teacher Education, Tehran 15614, Iran e-mail: hmousavi@iasbs.ac.ir
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A group G is called co-Dedekindian if every subgroup of G is invariant under all central automorphisms of G. In this paper we give some necessary conditions for certain finite p-groups with non-cyclic abelian second centre to be co-Dedekindian. We also classify 3-generator co-Dedekindian finite p-groups which are of class 3, having non-cyclic abelian second centre with |\Omega_1(G^p)|=p.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 1 , January 2002 , pp. 1 - 8
Copyright
2002 Glasgow Mathematical Journal Trust

Footnotes

This research was in part supported by a grant from IPM.