A short exact sequence of groups 0⟶A⟶B⟶C⟶0 is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct a commutative diagram as diagrammed above, where i is the injection of the first summand A and p is the projection onto the second summand C, and the vertical maps are isomorphisms.

commutative diagram | direct sum | short exact sequence