THE COMPLEXITY OF CHECKING IDENTITIES OVER FINITE GROUPS
Gábor Horváth, Csaba Szabó · International Journal of Algebra and Computation · 2006
We analyze the computational complexity of solving a single equation and checking identities over finite meta-abelian groups. Among others we answer a question of Goldmann and Russel from 1998: we prove that it is decidable in polynomial time whether or not an equation over the six-element group S 3 has a solution.