Let 𝐺 be a connected reductive group defined over Fq. Fix an integer M≥2, and consider the power map x↦xM on 𝐺. We denote the image of G(Fq) under this map by G(Fq)M and estimate what proportion of regular semisimple, ...
In this paper, we compute powers in the wreath product G≀SnG≀Sn for any finite group 𝐺. For r≥2r≥2 a prime, consider ωr:G≀Sn→G≀Snωr:G≀Sn→G≀Sn defined by g↦grg↦gr . Let Pr(G≀Sn):=|ωr(G≀Sn)
Consider the set of all powers GL(n, q)M = {xM ∣ x ∈ GL(n, q)} for an integer M ≥ 2. In this article, we aim to enumerate the regular, regular semisimple and semisimple elements as well as conjugacy classes in the set GL(n, ...