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On Mennicke Groups of Deficiency Zero II

Published online by Cambridge University Press:  20 November 2018

Muhammad A. Albar  and
Abdul-Aziz A. Al-Shuaibi
Muhammad A. Albar
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
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Abstract

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Let M be the group defined by the presentation 〈 x, y, z | xy = xm, yz = yn, zx = zr〉,m,n,r ∊ Z. M is one of the few 3-generator finite groups of deficiency zero. These groups have been considered by Mennicke [3], Macdonald, Wamsley [10], Johnson and Robertson [7], and Albar. Properties like the order of M, the nilpotency and solvability were studied. In this paper we give a better upper bound for M than the one given by Johnson and Robertson [7]. We also describe the structure of some cases of M.

Keywords

20F05Presentation of a groupsplit extensionTietze transformationReidemeister- Schreier process
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 289 - 293
Copyright
Copyright © Canadian Mathematical Society 1991

References

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