Zero Divisors of Support Size 3 in Complex Group Algebras of Finite Groups

Abstract

It is proved that if 1 + x + y or 1 + x − y cannot occur as a zero divisor of the complex group algebra of a finite group G for any two distinct x, y ∈ G \ {1}, then G is solvable. We also characterize all finite abelian groups with the latter property. The motivation of studying such property for finite groups is to settle the existence of zero divisors with support size 3 in the integral group algebra of torsion free residually finite groups. © 2025 Academic Center for Education, Culture and Research TMU.