Presentations of the Groups SL(2, m) And PSL(2, m)
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1129-1131
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In this paper, we refine the presentations of Behr and Mennicke [1] for SL(2, m) and PSL(2, m) where m is odd. The group SL(2, m) is first shown to be presented by the following system of generators and relations: 1.1 The group PSL(2, m) appears as the factor group 1.2 This simplification then permits us to use the results of Schur [3] to establish three-relation presentations for these groups.
Sunday, J. G. Presentations of the Groups SL(2, m) And PSL(2, m). Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1129-1131. doi: 10.4153/CJM-1972-118-x
@article{10_4153_CJM_1972_118_x,
author = {Sunday, J. G.},
title = {Presentations of the {Groups} {SL(2,} m) {And} {PSL(2,} m)},
journal = {Canadian journal of mathematics},
pages = {1129--1131},
year = {1972},
volume = {24},
number = {6},
doi = {10.4153/CJM-1972-118-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-118-x/}
}
[1] 1. Behr, H. and Mennicke, J., A Presentation of the groups PSL(2, p), Can. J. Math. 20 (1968), 1432–1438. Google Scholar
[2] 2. Gunning, R. C., Lectures on modular forms (Princeton University Press, Princeton, 1962). Google Scholar
[3] 3. Schur, J., Untersuchungen uber die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 132 (1907), 85–137. Google Scholar
[4] 4. Zassenhaus, H. J., A Presentation of the groups PSL(2, p) with three defining relations, Can. J. Math. 21 (1969), 310–311. Google Scholar
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