In the present paper, by using a map namely, p~\documentclass[12pt]{minimal}
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\begin{document}$$ \tilde{p} $$\end{document}-map on a group G, we have given a right loop T=p~(g):g∈G\documentclass[12pt]{minimal}
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\begin{document}$$ T = \left\{ {\tilde{p}(g):g \in G} \right\} $$\end{document} for a fixed subgroup K=g:p~(g)=e\documentclass[12pt]{minimal}
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\begin{document}$$ K = \left\{ {g:\tilde{p}(g) = e} \right\} $$\end{document} of G. This T becomes a group under some certain conditions. (T, K, σ\documentclass[12pt]{minimal}
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\begin{document}$$ \sigma $$\end{document}, f), is a c-groupoid. There is a group extension G of group K with T as right transversal to K in G such that (T, K, σ\documentclass[12pt]{minimal}
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\begin{document}$$ \sigma $$\end{document}, f) is c-groupoid associated with the extension G.
