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January 2003 (p,q,r)-Generations and nX-Complementary Generations of the Thompson Group Th
Ali Reza Ashrafi
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SUT J. Math. 39(1): 41-54 (January 2003). DOI: 10.55937/sut/1059541213


A group G is said to be (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 1993 J. Moori posed the question of finding all triples (l,m,n) such that a given non-abelian finite simple group is (l,m,n)-generated. In this paper we partially answer this question for the Thompson group Th. In fact we study (p,q,r)-generation, where p, q and r are distinct primes, and nX-complementary generations of the Thompson group Th.


The author would like to thank the referee for his/her helpful remarks. He also would like to thank the University of Kashan for the opportunity of taking a sabbatical leave during which this work was done, and the Department of Mathematics of UMIST for its warm hospitality.


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Ali Reza Ashrafi. "(p,q,r)-Generations and nX-Complementary Generations of the Thompson Group Th." SUT J. Math. 39 (1) 41 - 54, January 2003.


Received: 30 October 2002; Revised: 8 June 2003; Published: January 2003
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1059541213

Primary: 20D08 , 20F05

Keywords: (p,q,r)-generation , nX-complementary generation , sporadic group , Thompson group , triangle group

Rights: Copyright © 2003 Tokyo University of Science

Vol.39 • No. 1 • January 2003
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