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arXiv · 1308.4290

Twisted Automorphisms of Right Loops

R Lal·A. C. Yadav
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Abstract

In this paper we make an attempt to study right loops $(S, o)$ in which, for each $y\in S$, the map $σ_y$ from the inner mapping group $G_S$ of $(S, o)$ to itself given by $σ_y (h)(x) o\ h(y)= h(xoy)$, $x\in S, h\in G_S$ 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. A representation theorem for twisted right gyrogroup is established. We also study relationship between twisted gyrotransversals and twisted subgroups (a concept which arose as a tool to study computational complexity involving class NP).

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R Lal, A. C. Yadav. 2013-08-20. Twisted Automorphisms of Right Loops. https://arxiv.org/abs/1308.4290

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