In this paper we make an attempt to study right loops (S, o) in which, for each y is an element of S, the map sigma(y) from the inner mapping group G(S) of (S, o) to itself given by sigma(y)(h)(x) o h(y) = h(xoy), x is an element of S, h is an element of 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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