The Herzog-Schönheim conjecture for simple and symmetric groups
M. Garonzi, L. Margolis
公開日: 2025/9/29
Abstract
The Herzog-Sch\"onheim 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.