G is a group acting on S. H is a subgroup of G and let s be anything in S. Is it true that the order of s under action of G is divisible by the order of s under action of H?
Orbit of a subgroup
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$\begingroup$
group-theory
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5Can you tell us what you've already tried? And what concepts/techniques/theoerems you think might be involved? – 2011-05-16
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0that its true if every action of G is unique. $|G|$/$|G_s|$=$m|H|/k|H_s|$ – 2011-05-16
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0The stabilizer $H_s$ of $s$ in $H$ is exactly the intersection $G_s \cap H$. So your statement is reduced to ask if $[H \cap G:H \cap G_s] / [G:G_s]$. Any ideas on how to go further? – 2011-05-16