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On conjugacy p-separability of free centre-by-metabelian groups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

C. K. Gupta ,
N. D. Gupta  and
F. Levin
C. K. Gupta
Affiliation:
Department of Mathematics, Ruhr UniversityBochum West, Germany
N. D. Gupta
Affiliation:
Department of Mathematics, University of ManitobaWinnipeg R3T 2N2, Canada
F. Levin
Affiliation:
Department of Mathematics, University of ManitobaWinnipeg R3T 2N2, Canada
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Abstract

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A group G is said to be conjugacy p-separable if two non-conjugate elements of G remain non-conjugate in some finite p-group endomorphic image of G. We show that the non-cyclic free centre-by-metabelian groups are not conjugacy p-separable for any prime p. On the other hand, we show that every free centre-by-metabelian group has the solvable conjugacy problem

MSC classification

Secondary: 20E22: Extensions, wreath products, and other compositions 20E25: Local properties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 2 , October 1989 , pp. 334 - 342
Copyright
Copyright © Australian Mathematical Society 1989

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