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dc.contributor.advisor Basheer, A. B. M. Motalane, Malebogo John 2022-06-28T10:55:35Z 2022-06-28T10:55:35Z 2021
dc.description Thesis (Ph.D. (Mathematics)) -- University of Limpopo, 2021 en_US
dc.description.abstract 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 en_US
dc.description.sponsorship University of Limpopo en_US
dc.format.extent 131 leaves en_US
dc.language.iso en en_US
dc.relation.requires PDF en_US
dc.subject (p.g.r)-generations en_US
dc.subject Prime numbers en_US
dc.subject.lcsh Existence theorems en_US
dc.subject.lcsh Error functions en_US
dc.subject.lcsh Finite groups en_US
dc.subject.lcsh Numbers, Prime en_US
dc.title (p,g,r) - generations and conjugacy class ranks of certain simple groups of the form, Sp(,2), M23 and A11 en_US
dc.type Thesis en_US

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