Groups having three complex irreducible character degrees
A study is made of the possible sets \(\{1,a,b\}\) consisting of exactly three character degrees. A lot of results was already known. For instance, all the corresponding groups are solvable of derived length \(\leq 3\). Here we see that if \((a,b) =1\), only certain subgroups of affine semi-linear groups and cyclic semi-direct extensions of extraspecial \(p\)-groups occur here in essence. Also the corresponding arithmetical conditions on \(a\), \(b\) are given. There are much other results in this paper, with full proofs and arguments. It is a paper suitable for (advanced) students to study.
scientific article; zbMATH DE number 794341