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Characterizing projective general unitary groups PGU 3 ( q 2 ) by their complex group algebras

Farrokh Shirjian, Ali Iranmanesh (2017)

Czechoslovak Mathematical Journal

Let G be a finite group. Let X 1 ( G ) be the first column of the ordinary character table of G . We will show that if X 1 ( G ) = X 1 ( PGU 3 ( q 2 ) ) , then G PGU 3 ( q 2 ) . As a consequence, we show that the projective general unitary groups PGU 3 ( q 2 ) are uniquely determined by the structure of their complex group algebras.

Characters of finite quasigroups VII: permutation characters

Kenneth Walter Johnson, Jonathan D. H. Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

Each homogeneous space of a quasigroup affords a representation of the Bose-Mesner algebra of the association scheme given by the action of the multiplication group. The homogeneous space is said to be faithful if the corresponding representation of the Bose-Mesner algebra is faithful. In the group case, this definition agrees with the usual concept of faithfulness for transitive permutation representations. A permutation character is associated with each quasigroup permutation representation,...

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