Thesis (Ph.D. (Mathematics)) -- University of Limpopo, 2021 / A finite group G is called (l, m, n)-generated, if it is a quotient group of the triangle group
T(l, m, n) = x, y, z|xl = ym = zn = xyz = 1-. In [43], Moori posed the question of finding all
the (p, q, r) triples, where p, q and r are prime numbers, such that a non-abelian finite simple group G is a (p, q, r)-generated. In this thesis, we will establish all the (p, q, r)-generations of the following groups, the Mathieu sporadic simple group M23, the alternating group A11 and the symplectic group Sp(6, 2). Let X be a conjugacy class of a finite group G. The rank of X in G, denoted by rank(G : X), is defined to be the minimum number of elements of X generating G. We investigate the ranks of the non-identity conjugacy classes of the above three mentioned finite simple groups. The Groups, Algorithms and Programming (GAP) [26] and the Atlas of finite group representatives
[55] are used in our computation / University of Limpopo
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ul/oai:ulspace.ul.ac.za:10386/3845 |
| Date | January 2021 |
| Creators | Motalane, Malebogo John |
| Contributors | Basheer, A. B. M. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 131 leaves |
| Relation |
Page generated in 0.002 seconds