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Polygonal products of polycyclic by finite groups

Published online by Cambridge University Press:  17 April 2009

R.B.J.T. Allenby
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom, e-mail: PMT6RA@LEBDS.AC.UK
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Abstract

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We prove that a polygonal product of polycyclic by finite groups amalgamating normal subgroups, with trivial mutual intersections, is cyclic subgroup separable. Because of a recent example (stated below) of the author this substantial improvement on a recent theorem of Kim is essentially best possible.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Allenby, R.B.J.T., ‘The residual finiteness of polygonal products – two counterexamples’, Canad. Math. Bull. 37 (1994), 433436.CrossRefGoogle Scholar
[2]Allenby, R.B.J.T. and Gregorac, R.J., ‘On locally extended residually finite groups’, in Lecture Notes in Mathematics 319 (Springer-Verlag, Berlin, Heidelberg, New York, 1973), pp. 917.Google Scholar
[3]Allenby, R.B.J.T. and Tang, C.Y., ‘On the residual finiteness of certain polygonal products’, Canad. Math. Bull. 32 (1989), 1117.CrossRefGoogle Scholar
[4]Baumslag, G., ‘On the residual finiteness of generalized free products of nilpotent groups’, Trans. Amer. Math. Soc. 106 (1963), 193209.CrossRefGoogle Scholar
[5]Gruenberg, K.W., ‘Residual properties of infinite soluble groups’, Proc. London Math. Soc. 7 (1957), 2962.CrossRefGoogle Scholar
[6]Higman, G., ‘A finitely generated infinite simple group’, J. London Math. Soc. 26 (1951), 6164.CrossRefGoogle Scholar
[7]Kim, Goansu, ‘On polygonal products of finitely generated Abelian groups’, Bull. Austral. Math. Soc. 45 (1992), 453462.CrossRefGoogle Scholar
[8]Kim, Goansu, ‘Cyclic subgroup separability of generalized free products’, Canad. Math. Bull. 36 (1993), 296302.CrossRefGoogle Scholar
[9]Neumann, B.H., ‘An essay on free products of groups with amalgamations’, Proc. Roy. Soc. Ser. A 246 (1954), 503554.Google Scholar
[10]Stebe, P., ‘Residual finiteness of a class of knot groups’, Comm. Pure Appl. Math. 21 (1968), 563583.CrossRefGoogle Scholar