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One-relater groups with center

Published online by Cambridge University Press:  09 April 2009

Stephen Meskin ,
A. Pietrowski  and
Arthur Steinberg
Stephen Meskin
Affiliation:
Department of Mathematics The University of Connecticut StorrsConn. 06268 U.S.A.
A. Pietrowski
Affiliation:
Department of Mathematics University of Toronto Canada.
Arthur Steinberg
Affiliation:
Department of Mathematics Queens CollegeCUNY Flushing, New York, 11367 U. S. A.
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Abstract

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Many one-relator groups with center have been shown to be of the form A necessary and a sufficient condition for the sequence (P1, Q1, P2, Q2,…,Pt, Qt) are given in order for groups of the above form to be one-relator groups.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 3 , November 1973 , pp. 319 - 323
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Baumslag, G., and Taylor, T., ‘The centre of groups with one defining relator’, Math. Ann. 175 (1968), 315–319.Google Scholar
[2]Karrass, A., Magnus, W., and Solitar, D., ‘Elements of finite order in groups with a single defining relation’, Comm. Pure Appl. Math. (1960), 57–66.Google Scholar
[3]Magnus, W., Karrass, A., and Solitar, D., Combinatorial group theory, Pure and Appl. Math., Vol. 13 (Interscience, New York, 1966).Google Scholar
[4]Murasugi, K., ‘The center of a group with a single defining relation’, Math. Ann. 155, (1964), 246–251.Google Scholar
[5]Pietrowski, A., Thesis (in preparation). (University of Toronto).Google Scholar