Martyn Quick

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math.GR2026

The probability of generating finite and profinite groups

Scott Harper, Martyn Quick

Famously, every finite simple group $G$ can be generated by a pair of elements. Moreover, Liebeck and Shalev (1995) proved that the probability that a pair of elements generate $G$ …

math.GR2025

Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups

Jiaping Lu, Martyn Quick

Let $G_{1}$ , $G_{2}$ , ... be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group and construct a sequence $(W_{i})$ of wreath pro…