en عمومى General پژوهشي Research paper <div style="margin: 0px; text-indent: 0px; text-align: justify;">It is proved that if <em>1 + x + y</em> or <em>1 + x - y</em> cannot occur as a zero divisor of the complex group algebra of a finite group <em>G</em> for any two distinct <em>x, y &isin; G {1}</em>, then <em>G</em> 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.</div> Zero divisors, Complex group algebras, Finite groups. 123 128 http://ijmsi.ir/browse.php?a_code=A-10-6360-1&slc_lang=en&sid=1 Alireza Abdollahi a.abdollahi@math.ui.ac.ir 100319475328460011738 100319475328460011738 Yes Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746-73441, Iran Mahdi Ebrahimi m.ebrahimi.math@ipm.ir 100319475328460011739 100319475328460011739 No Institute for Research in Fundamental Sciences, School of Mathematics, Tehran, Iran