What question did this study set out to answer?

The aim is to address J. Moori's question on finding triples (l, m, n) for non-abelian finite simple groups.

April 3, 2026Open Access

(p,q,r)-Generations and nX-Complementary Generations of the Thompson Group Th

Puntos clave

The aim is to address J. Moori's question on finding triples (l, m, n) for non-abelian finite simple groups.
Studied (p, q, r)-generation where p, q, r are distinct primes.
Analyzed nX-complementary generations of the Thompson group Th.
Partially answered the question posed by Moori regarding generation of the Thompson group.
Provided insights into the structure of (p, q, r)-generation for distinct primes.

Resumen

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|x l = y m = z n = 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 T h.In fact we study (p, q, r)-generation, where p, q and r are distinct primes, and nX-complementary generations of the Thompson group T h.

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