Lehmer Sequences in Finite Groups

Abstract

We study the Lehmer sequences modulo m. Moreover, we define the Lehmer orbit and the basic Lehmer orbit of a 2-generator group G for a generating pair (x, y) ∈ G and examine the lengths of the periods of these orbits. Furthermore, we obtain the Lehmer lengths and the basic Lehmer lengths of the Fox groups G 1,t for t ≥ 3.