Practice problem
Let GGG be a group and let G2G^2G2 denote the subset of squares of GGG. What can you say about G2G^2G2?
G2G^2G2 is a normal subgroup of GGG.
G2G^2G2 generates a subgroup HHH of GGG, which may or may not be normal in GGG.
G2G^2G2 generates a subgroup NNN of GGG, with the property that the kernel of a homomorphism G→HG\to HG→H contains NNN whenever HHH is 222-torsion (i.e. h2=1h^2 = 1h2=1 for all h∈Hh\in Hh∈H).
Type a concept, like “slope” or “photosynthesis”.