Applications of a graph related to conjugacy classes in finite groups
A recent result of B. Huppert states that if the set of character degrees of a finite group is \(\{\) 1,2,3,...,k\(\}\) then \(k=1,2,3,4,6\). Moreover, a description of the groups for each possible k is given. Here the authors consider the analogous problem for conjugacy classes lengths and describe groups in which the lengths of the noncentral classes are consecutive integers. The proof uses the study of a graph related to conjugacy classes that was considered by Bertram, Herzog and Mann. Another application of this graph which is included here is to give a different (shorter) proof to a result of Chillag and Herzog on groups in which all noncentral classes have prime power lengths.
scientific article; zbMATH DE number 4191985