Extension of Groups Using $$ \tilde{p} $$ p ~ -maps

Abstract

In the present paper, by using a map namely, \( \tilde{p} \) -map on a group G, we have given a right loop \( T = \left\{ {\tilde{p}(g):g \in G} \right\} \) for a fixed subgroup \( K = \left\{ {g:\tilde{p}(g) = e} \right\} \) of G. This T becomes a group under some certain conditions. (T, K, \( \sigma \) , 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, \( \sigma \) , f) is c-groupoid associated with the extension G.

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