Geodesic
On Mennicke Groups of Deficiency Zero II
Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 289-293

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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.
DOI : 10.4153/CMB-1991-046-5
Mots-clés : 20F05, Presentation of a group, split extension, Tietze transformation, Reidemeister- Schreier process 
Albar, Muhammad A. On Mennicke Groups of Deficiency Zero II. Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 289-293. doi: 10.4153/CMB-1991-046-5
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     title = {On {Mennicke} {Groups} of {Deficiency} {Zero} {II}},
     journal = {Canadian mathematical bulletin},
     pages = {289--293},
     year = {1991},
     volume = {34},
     number = {3},
     doi = {10.4153/CMB-1991-046-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-046-5/}
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