The \(2\)-characters of a group and the group determinant (Q1902968)

This instructional paper gives among others, the following results. (1) The pairs of non-isomorphic groups of order \(p^3\), \(p\) odd prime, having the same irreducible 2-characters; (2) Results are given on the \(k\)-characters of the regular representation; (3) A shorter proof of the Johnson-Sehgal result that pairs of non-isomorphic groups exist with the same irreducible 1- and 2-characters; (4) Older results are compared with new ones obtained here. The style of writing is very eluminating and as such the paper contains a lot of facts worthwhile to be developed.