Title: Nonequational Stable Groups,
Abstract: We introduce a combinatorial criterion for verifying whether a formula is not
the conjunction of an equation and a co-equation. Using this, we give a
transparent proof for the nonequationality of the free group, which was
originally proved by Sela. Furthermore, we extend this result to arbitrary free
products of groups (except $\mathbb{Z}_2*\mathbb{Z}_2$), providing an abundance
of new stable nonequational theories.