Let H be a subgroup of finite index in G. Show that the intersection of all conjugates of H is a normal subgroup of finite index in G.

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- Apr 2nd 2013, 04:40 PMhenderson7878abstract algebra subgroups of finite index
Let H be a subgroup of finite index in G. Show that the intersection of all conjugates of H is a normal subgroup of finite index in G.

- Apr 2nd 2013, 05:42 PMjohngRe: abstract algebra subgroups of finite index
The intersection is obviously normal. There are only finitely many conjugates (why?). The intersection of 2 subgroups of finite index is of finite index, and by induction the intersection of finitely many subgroups of finite index has finite index -- needs proof, I guess. So the intersection of the finitely many conjugates is of finite index.

Until I see some evidence of effort on your part, this is the last response I will make to a question. This is the third question of yours I've answered with no input from you.