In this paper we make an attempt to study right loops (S,o) in which, for eachy ∈ S, the map σyfrom the inner mapping groupGSof (S,o) to itself given by σy(h)(x)o h(y) = h(xoy),x ∈ S,h ∈ GSis 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. [ABSTRACT FROM PUBLISHER]
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