1. The problem statement, all variables and given/known data
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] .
3. 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.
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] .
3. 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.
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