Question
Asked Oct 17, 2019
Let H and K be subgroups of a group G and assume |G : H| < +co. Show that
|K Kn H G H\
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Let H and K be subgroups of a group G and assume |G : H| < +co. Show that |K Kn H G H\

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Step 1

Let G be a group and let H and k be two subgroup of G.

Ass...

Since knH k<G and kNH <H <G.
Therefore [G:knH]-[G:HH:kH]
Since, [G H is finite, therefore [G: kNH is also finite
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Since knH k<G and kNH <H <G. Therefore [G:knH]-[G:HH:kH] Since, [G H is finite, therefore [G: kNH is also finite

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