The authors prove the Herzog-Schönheim conjecture on coset partitions for all simple groups and all symmetric groups.
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NG(E) equals NGad(E) in E7(q) if and only if q ≡ ±1 mod 8.
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The Herzog-Sch\"onheim conjecture for simple and symmetric groups
The authors prove the Herzog-Schönheim conjecture on coset partitions for all simple groups and all symmetric groups.
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Structure of an exotic $2$-local subgroup in $E_7(q)$
NG(E) equals NGad(E) in E7(q) if and only if q ≡ ±1 mod 8.