Extension of Groups Using \( \tilde{p} \)-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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Correspondence to Punish Kumar.

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Srivastava, S., Kumar, P. Extension of Groups Using \( \tilde{p} \)-maps. Natl. Acad. Sci. Lett. 42, 525–528 (2019). https://doi.org/10.1007/s40009-019-0788-5

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Keywords

  • \( \tilde{p} \)-map
  • Right transversal
  • Right loop
  • c-groupoid
  • Group