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A Characterization of Group Through Isomorphism Classes of Transversals

Group Theory 2024-01-09 v2

Abstract

Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index of H in G is 6 and the permutation representation of G on right cosets of H in G is isomorphic to the alternating group on four symbols.

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Cite

@article{arxiv.2306.13363,
  title  = {A Characterization of Group Through Isomorphism Classes of Transversals},
  author = {Vivek Kumar Jain and Raja Rawat},
  journal= {arXiv preprint arXiv:2306.13363},
  year   = {2024}
}

Comments

some corrections are to be made