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## Homework Statement

H is a subgroup of G, and a and b are elements of G.

Show that Ha=Hb iff [itex] ab^{-1} \in H [/itex] .

## The Attempt at a Solution

line 1: Then a=1a=hb for some h in H.

then we multiply both sides by b inverse.

and we get [itex] ab^{-1}=h [/itex]

This is a proof in my book.

My question is on line 1 when they write 1a, is 1 the identity element in H.

So basically Ha=1a and this trick allows the rest to follow.