The Herzog-Schönheim conjecture for simple and symmetric groups

Fuente: arXiv
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Main Authors: Garonzi, M., Margolis, L.
Format: Preprint
Published: 2025
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author Garonzi, M.
Margolis, L.
author_facet Garonzi, M.
Margolis, L.
contents The Herzog-Schönheim conjecture states that if $H_1, \ldots, H_k$ are subgroups of a group $G$ and $x_1, \ldots, x_k$ are elements of $G$ such that $H_1x_1, \ldots, H_kx_k$ is a partition of $G$ into cosets, then two of these subgroups must have the same index. We prove this conjecture for simple groups and for symmetric groups.
format Preprint
id arxiv_https___arxiv_org_abs_2509_25118
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Herzog-Schönheim conjecture for simple and symmetric groups
Garonzi, M.
Margolis, L.
Group Theory
20D60, 20B30, 20D05
The Herzog-Schönheim conjecture states that if $H_1, \ldots, H_k$ are subgroups of a group $G$ and $x_1, \ldots, x_k$ are elements of $G$ such that $H_1x_1, \ldots, H_kx_k$ is a partition of $G$ into cosets, then two of these subgroups must have the same index. We prove this conjecture for simple groups and for symmetric groups.
title The Herzog-Schönheim conjecture for simple and symmetric groups
topic Group Theory
20D60, 20B30, 20D05
url https://arxiv.org/abs/2509.25118