group homomorphism
function between groups that preserves multiplication structure
group representation
group homomorphism into the general linear group over a vector space
parity of a permutation
group homomorphism from the symmetric group over a finite set to the two-element group {±1}
projective representation
homomorphism G → PGL(V) from a group G to a projective linear group PGL(V) over a vector space V
multiplicative character
group homomorphism to the multiplicative group of a field
One-parameter group
Lie group homomorphism from the real numbers
group isomorphism
bijective group homomorphism
J-homomorphism
special homomorphism from a homotopy group of a special orthogonal group to a homotopy group of spheres