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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Originally Posted by jzellt 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! So we want to show that let Then for some By the relation we know that there exists an such that and we know that by there exists an such that Putting all of these together we get Now you just need to show or justify the other direction (it is exactly the same.)
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