Following S. Brick, a 2-complex X is called "Kervaire" if all systems of equations, with coefficients in arbitrary groups G and the attaching maps of X as the words in the variable letters, are solvable in an over group of G. An obstruction theory is developed for solving equations modeled on Z = Xp Y, where X and Y are Kervaire 2-complexes and T is a subgraph of Z^\ each connected component of...