# Left and right cosets (modern Algebra)

• April 6th 2013, 06:20 AM
mohammedlabeeb
Left and right cosets (modern Algebra)
Let H be a subgroup of G, and let S={left cosets of H in G}, and T={Right cosets of H in G}. Now Define f: S-->T, by the following function f(aH)=H(a^-1)
Prove that f is well define!!!

All I know is "A well defined set is that if aH = bH then f(aH) = f(bH)"

$Ha^{-1}=Hb^{-1}$ iff $Ha^{-1}b=H$