Advertisement

Extension of Groups Using \( \tilde{p} \)-maps

  • Swapnil Srivastava
  • Punish KumarEmail author
Short Communication

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.

Keywords

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

Notes

References

  1. 1.
    Lal R (1996) Transversals in groups. J Algebra 181:70–81MathSciNetCrossRefGoogle Scholar
  2. 2.
    Srivastava S, Kumar P (2014) On the p-maps of groups. Math Stat 2(6):214–218Google Scholar
  3. 3.
    Srivastava S, Kumar P (2014) H-transversals in H-groups. Int J Algebra 8(15):705–712CrossRefGoogle Scholar

Copyright information

© The National Academy of Sciences, India 2019

Authors and Affiliations

  1. 1.Department of MathematicsECCAllahabadIndia
  2. 2.Government Polytechnic, ShahbadRampurIndia

Personalised recommendations