Question

Let G be a group, and H a subgroup of G, let a,b?G prove the statement or give a counterexample:

If aH=bH, then Ha=Hb

Answer #1

The solution is attached.

Let
G be a finite group and H a subgroup of G. Let a be an element of G
and aH = {ah : h is an element of H} be a left coset of H. If B is
an element of G as well show that aH and bH contain the same number
of elements in G.

if
H is a subgroup of G and Ha=Hb where a,b e G, does it follow that
aH=bH? Support your answer.
Show every step.

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