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arXiv · 1307.5392

A Note On Transversals

Vivek Kumar Jain
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Abstract

Let $G$ be a finite group and $H$ a core-free subgroup of $G$. We will show that if there exists a solvable, generating transversal of $H$ in $G$, then $G$ is a solvable group. Further, if $S$ is a generating transversal of $H$ in $G$ and $S$ has order 2 invariant sub right loop $T$ such that the quotient $S/T$ is a group. Then $H$ is an elementary abelian 2-group.

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Vivek Kumar Jain. 2013-07-20. A Note On Transversals. https://doi.org/10.1515/ausm-2017-0013

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