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Groups which are an infinite cyclic extension of a unique base group

Published online by Cambridge University Press:  09 April 2009

A. M. Brunner ,
James McCool  and
Alfred Pietrowski
A. M. Brunner
Affiliation:
Department of Mathematics, York University, Downsview, Ontario, Canada.
James McCool
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada.
Alfred Pietrowski
Affiliation:
Department of Mathematics, York University, Downsview, Ontario, Canada.
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Let G be a group which has exactly one normal subgroup N with G/N infinite cyclic; clearly such a group is an HNN group with base N and stable letter t, where t induces an automorphism θ, of N under conjugation. We call such a group G a unique base group with automorphism θ, and base N.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 499 - 503
Copyright
Copyright © Australian Mathematical Society 1977

References

Brunner, A. M. (1974), ‘Transitivity-systems of certain one-relator groups’, Proc. Second Internat. Conf. Theory of Groups, Canberra 1973 (Lecture Notes in Mathematics, 372, 131–140. Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
Magnus, Wilhelm, Karrass, Abraham, Solitar, Donald (1966), Combinatorial Group Theory (Pure and Appl. Math. 13. Interscience [John Wiley & Sons], New York, London, Sydney, 1966).Google Scholar
Moldavanski, D. I. (1967), ‘Certain subgroups of groups with one defining relation’, Siberian Math. J. 8, 1039–1048 (1968).CrossRefGoogle Scholar
Rapaport, Elvira Strasser (1959), ‘Note on Nielsen transformations’, Proc. Amer. Math. Soc. 10, 228–235.CrossRefGoogle Scholar