In mathematics, a group G is called the direct sum of two subgroups H₁ and H₂ if

More generally, G is called the direct sum of a finite set of subgroups {H_i} if

If G is the direct sum of subgroups H and K, then we write G = H + K; if G is the direct sum of a set of subgroups {H_i}, we often write G = ∑H_i. Loosely speaking, a direct sum is isomorphic to a weak direct product of subgroups.