This is a proof I am struggling on ...(adsbygoogle = window.adsbygoogle || []).push({});

Let H be a subgroup of the permutation of n and let A equal the intersection of H and the alternating group of permutation n. Prove that if A is not equal to H, than A is a normal subgroup of H having index two in H.

My professor gave me the hint to begin by letting g be in H but not in A and then showing that gA and A are two cosets of A in H.

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# Homework Help: Proof on Normal Subgroups and Cosets in Group Theory

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