Let G be any group such that
G≅G/H
where H is a normal subgroup of G.If G is finite, then H is the trivial subgroup {e}. Does the result still hold when G is infinite ? In what kind of group could I search for a counterexample ?
Answer
Look at G=∞⨁i=1 Z and the subgroup H=Z ⊕ ∞⨁i=2 0.
Attribution
Source : Link , Question Author : Klaus , Answer Author : Rasmus
