On the Herzog-Schönheim conjecture for uniform covers of groups

Zhi-Wei Sun

Let G be any group and $a_1{G}_1,...,a_k{G}_k(k>1)$ be left cosets in G. In 1974 Herzog and Schönheim conjectured that if $\Cal A=\{a_iG_i\}_{i=1}^k$ is a partition of G then the (fin…