Automorphisms of orthogonal decompositions and of group algebras of groups with partitions

Abstract

This article is devoted to an investigation of the following conjecture. If is a family of subgroups that partition a finite group , then every automorphism of the group algebra that permutes the subalgebras also permutes the lines , . The conjecture is confirmed for the following classes of groups with partitions: 1) Abelian groups; 2) non-Abelian 2-groups; 3) Frobenius groups with partitions inscribed in the standard partitions (consisting of the kernel together with all complements); 4) -groups; 5) and ; 6) the Suzuki groups . This result confirms the conjecture concerning the finiteness of the automorphism groups of orthogonal decompositions constructed from the groups with partition occurring in the above list.