Masters Examination in Mathematics

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Solution: For the action mentioned in the hint, the stabilizer of the coset eH (e is the identity) is H since gH = H implies that g ∈ H. The kernel K of the homomorphism of G into the permutation group of the cosets is a normal subgroup of G which is the intersection of stabilizers of all cosets. In particular the kernel K of the above homomorphism is a subgroup of H. Its index in G is equal to the order of the subgroup of permutation group of cosets which is the image of the above homomorphism and hence has order less that n!.

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Masters Examination in Mathematics

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تاریخ انتشار 2009