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arXiv · 2306.13363

A Characterization of Group Through Isomorphism Classes of Transversals

Vivek Kumar Jain·Raja Rawat
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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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Vivek Kumar Jain, Raja Rawat. 2023-06-23. A Characterization of Group Through Isomorphism Classes of Transversals. https://arxiv.org/abs/2306.13363

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