Groups which do not possess characters of nontrivial prime power degree. (Q2509498)

In this paper, the authors study groups in which the only prime power that occurs as an irreducible complex character degree is 1. The main result of the paper is that the nonabelian composition factors of such a group also have this property or are the sporadic simple group \(M_{12}\). All simple groups which have this property are known (and listed in the paper) by work of \textit{G. Malle} and \textit{A. E. Zalesskij} [Arch. Math. 77, No. 6, 461-468 (2001; Zbl 0996.20006)]. The authors also provide an example via GAP that the exception \(M_{12}\) really does occur.