Geodesic
A Class of Three-Generator, Three-Relation, Finite Groups
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 36-40

Voir la notice de l'article provenant de la source Cambridge University Press

Mennicke (2) has given a class of three-generator, three-relation finite groups. In this paper we present a further class of three-generator, threerelation groups which we show are finite.The groups presented are defined as: with α |γ| ≠ 1, β |γ| ≠ 1, γ ≠ 0.We prove the following result.THEOREM 1. Each of the groups presented is a finite soluble group.We state the following theorem proved by Macdonald (1).THEOREM 2. G 1(α, β, 1) is a finite nilpotent group. 1. In this section we make some elementary remarks. 
Wamsley, J. W. A Class of Three-Generator, Three-Relation, Finite Groups. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 36-40. doi: 10.4153/CJM-1970-004-5
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[1] 1. Macdonald, I. D., On a class of finitely presented groups, Can. J. Math. 14 (1962), 602–613. Google Scholar

[2] 2. Mennicke, J., Einige endliche Gruppen mit drei Erzeugenden und drei Relationen, Arch. Math. 10 (1959), 409–418. Google Scholar

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