Abstract
In this paper we make an attempt to study right loops (S, o) in which, for each y ∈ S, the map σ y from the inner mapping group G S of (S, o) to itself given by σ y (h)(x)o h(y) = h(xoy), x ∈ S, h ∈ G S is a homomorphism. The concept of twisted automorphisms of a right loop and also the concept of twisted right gyrogroup appears naturally and it turns out that the study is almost equivalent to the study of twisted automorphisms and a twisted right gyrogroup. We also study relationship between twisted gyrotransversals and twisted subgroups.
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