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arXiv · 2406.16184

Characters, Hall subgroups, and Normal Complements

Robert Guralnick·Gabriel Navarro
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Abstract

If $H$ is a Hall subgroup of a finite group $G$, it was proven in 1989 using the classification of finite simple groups that all the irreducible complex characters of $H$ extend to $G$ if and only if there is $N\trianglelefteq G$ such that $HN=G$ and $H\cap N=1$. In this note we offer a modular version of this result under more general hypothesis.

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Robert Guralnick, Gabriel Navarro. 2024-06-23. Characters, Hall subgroups, and Normal Complements. https://arxiv.org/abs/2406.16184

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