Given H is a subgroup of G and that H has finite index n, prove that there is a normal subgroup K of G such that and . Don't assume that G is finite.

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- Feb 18th 2011, 08:34 PMabhishekkgpnormal subgroups and cayley's theorem
Given H is a subgroup of G and that H has finite index n, prove that there is a normal subgroup K of G such that and . Don't assume that G is finite.

- Feb 18th 2011, 08:46 PMroninpro
Note that acts on the cosets of by left multiplication. Since there are cosets, this induces a homomorphism . Then we know that is a normal subgroup of .

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