Let L be a restricted Lie algebra with the restricted enveloping algebra u(L) over a perfect field of positive characteristic p. The restricted isomorphism problem asks what invariants of L are determined by u(L). This problem is the analogue of the modular isomorphism problem for finite p-groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacycl...

Abstract The Amit conjecture about word maps on finite nilpotent groups has been shown to hold for certain classes of groups. generalised says that the probability an element occurring in image a map group G is either 0, or at least 1/| |. Noting work Ashurst, we name Amit–Ashurst and show holds p -groups with cyclic maximal subgroup.