I know relation between normalizer of a subgroup $H$ of a group $G$ and the stabilizer of one point $x$ of a set $Ω$ on which the group acts. Given that$$ \gcd([G:\operatorname{Normalizer}(H)], [G:\operatorname{Stab}(x)])=1, $$ i.e.$$ G=\operatorname{Stab}(x) \operatorname{Normalizer}(H). $$ Now I put $H:=\operatorname{Stab}(x)$ and I do not have gcd. Can I write similar factorization?
2026-03-25 12:21:24.1774441284
Normalizer, stabilizer and orbits
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