Generating Triples of Involutions of Groups of Lie Type of Rank 2 Over Finite Fields

Abstract

For finite simple groups U₅(2ⁿ), n > 1, U₄(q), and S₄(q), where q is a power of a prime p > 2, q − 1 ≠= 0(mod4), and q ≠= 3, we explicitly specify generating triples of involutions two of which commute. As a corollary, it is inferred that for the given simple groups, the minimum number of generating conjugate involutions, whose product equals 1, is equal to 5.