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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

References

[1]Blackburn, N., ‘Conjugacy in nilpotent groups’, Proc. Amer. Math. Soc. 16 (1965), 143–148.CrossRefGoogle Scholar
[2]Gupta, C. K., ‘A faithful matrix representation for certain centre-by-metabelian groups’, J. Austral. Math. Soc. Ser. A 10 (1969), 451–464.CrossRefGoogle Scholar
[3]Gupta, C. K., “The free centre-by-metabelian groups”, J. Austral. Math. Soc. Ser. A 16 (1973), 294–299.CrossRefGoogle Scholar
[4]Gupta, C. K., Herfort, W. and Levin, F., ‘The conjugacy problem for centre-by-metabelian groups’, Arch Math. 52 (1989), 117–121.CrossRefGoogle Scholar
[5]Gupta, C. K. and Gupta, N. D., ‘Generalized Magnus embeddings and some applications’, Math. Z. 160 (1978), 75–87.CrossRefGoogle Scholar
[6]Gupta, N., ‘Free group rings’, Contemp. Math. 66 (1987).CrossRefGoogle Scholar
[7]Gupta, N. D., Hurley, T. C. and Levin, F., ‘On the lower central factors of free centre-by-metabelian groups’, J. Austral. Math. Soc. Ser. A 38 (1985), 65–75.CrossRefGoogle Scholar
[8]Gupta, N. and Levin, F., ‘Generating groups of certain soluble varieties’, J. Austral. Math. Soc. Ser. A 17 (1974), 222–233.CrossRefGoogle Scholar
[9]Lyndon, R. C. and Schupp, P. E., ‘Combinatorial group theory’, Ergeb. Math. Grenzgeb. 89 (1977).Google Scholar
[10]Matthews, J., ‘The conjugacy problem in wreath products and free metabelian groups’, Trans. Amer. Math. Soc. 121 (1966), 329–339.CrossRefGoogle Scholar
[11]Timoshenko, E. I., ‘Conjugacy in free metabelian groups’, Algebra i Logika 6 (1967), 89–94.Google Scholar
[12]Wehrfritz, B. A. F., ‘Two examples of soluble groups that are not conjugacy separable’, J. London Math. Soc. (2) 7 (1973), 312–316.CrossRefGoogle Scholar