Character tables of \(p\)-groups with derived subgroup of prime order. I.
This paper is the first in a sequence of three papers containing the substance of the author's thesis. Here the following is studied. Two character tables of finite groups are isomorphic if there exist a bijection for the irreducible characters and a bijection for the conjugacy classes that preserve all the character values. Necessary and sufficient conditions for two finite groups are given in order that they have isomorphic character tables. In the case of finite \(p\)-groups with derived subgroup of order \(p\), it is shown that the character tables can be classified by equivalence classes of certain homomorphisms of Abelian \(p\)-groups. In the other papers a purely combinatorial description of the isomorphism classes of character tables of \(p\)-groups \(P\) with \(|[P,P]|=p\) will be provided.
algorithms for constructing \(p\)-groups
scientific article; zbMATH DE number 5303141
scientific article