Let G be a group and H a subgroup of G. Let a, b in G. Prove the following:

If aH = Ha and bH = Hb, then (ab)H = H(ab).

Can someone show this please? Thanks a lot in advance!

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- Oct 31st 2012, 05:38 PMjzelltLeft and Right Cosets
Let G be a group and H a subgroup of G. Let a, b in G. Prove the following:

If aH = Ha and bH = Hb, then (ab)H = H(ab).

Can someone show this please? Thanks a lot in advance! - Oct 31st 2012, 06:08 PMTheEmptySetRe: Left and Right Cosets