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2016•Unpublished venueRequires access

2-Generation of Finite Simple Groups in GAP

Faryad Ali, Mohammed A. Al-Kadhi, Abdullah Aljouiee, Mohammed Ali Faya Ibrahim

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Abstract

Generation of finite simple groups by suitable subsets is of great importance and has been studied since the origin of group theory. A finite group G is called (l, m, n)-generated, if it is a quotient groupof the triangle group T(l, m, n) = ‹ x, y, z|xl = ym= zn = xyz = 1 ›. In this article, we study some routines in the computer algebra system GAP - Groups, Algorithms and Programmingto determine (p, q, r)-generations of a finite simple group and apply these techniques to compute such type of generations for the Fischer's largest sporadic simple group Fi'24, where p, q and r are prime divisors of the |Fi'24|.

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What this paper is about

Generation of finite simple groups by suitable subsets is of great importance and has been studied since the origin of group theory. A finite group G is called (l, m, n)-generated, if it is a quotient groupof the triangle group T(l, m, n) = ‹ x, y, z|xl = ym= zn = xyz = 1 ›. In this article, we study some routines in the computer algebra system GAP - Groups, Algorithms and Programmingto determine (p, q, r)-generations of a finite simple group and apply these techniques to compute such type of generations for the Fischer's largest sporadic simple group Fi'24, where p, q and r are prime divisors of the |Fi'24|.

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Available abstract

Generation of finite simple groups by suitable subsets is of great importance and has been studied since the origin of group theory. A finite group G is called (l, m, n)-generated, if it is a quotient groupof the triangle group T(l, m, n) = ‹ x, y, z|xl = ym= zn = xyz = 1 ›. In this article, we study some routines in the computer algebra system GAP - Groups, Algorithms and Programmingto determine (p, q, r)-generations of a finite simple group and apply these techniques to compute such type of generations for the Fischer's largest sporadic simple group Fi'24, where p, q and r are prime divisors of the |Fi'24|.

Key concepts: Classification of finite simple groups, Simple (philosophy), Simple group, Group (periodic table), Quotient, Finite group, Group of Lie type, Prime (order theory)

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