Brauer \(t\)-tuples.
Two non-isomorphic finite groups form a Brauer pair if their exist a bijection for the conjugacy classes and a bijection for the irreducible characters that preserve all the character values and the power map. Generalizing the definition of a Brauer pair the notion of a Brauer \(t\)-tuple is introduced. It is shown in this paper that Brauer \(t\)-tuples exist for any \(t\geq 2\), i.e., finite groups \(G_1,\dots,G_t\) exist such that \((G_i,G_j)\) is a Brauer pair for all \(1\leq i\neq j\leq t\). In [\textit{B. Eick} and \textit{J. Müller}, J. Algebra 304, No. 1, 286-303 (2006; Zbl 1124.20004)], it has been shown that for \(p\geq 5\) there are Brauer 4-tuples of \(p\)-groups of order \(p^5\). Here it is proved that for any \(t\geq 2\) and any \(p\geq 3\) there are Brauer \(t\)-tuples of \(p\)-groups of order \(p^n\) for \(n\) large enough.
scientific article; zbMATH DE number 5610484
scientific article