Characters of some finite groups of Lie type with a restriction containing a linear character once. (Q875102)

Let \(\chi\) be an irreducible character of a finite group \(G\). A subgroup \(H\) of \(G\) is called a \(\chi\)-subgroup if the restriction of \(\chi\) to \(H\) has at least one linear constituent of multiplicity 1. In the paper under review the author considers some finite groups \(G\) of Lie type, i.e. \(\text{Sp}(4,2^f)\), \(G_2(q)\), \(Sz(q)\), \(Re(q)\), and a Sylow \(p\)-subgroup \(H\) of \(G\) where \(q\) is a power of \(p\) or \(p=2\) in the case of the symplectic group, and then determines the irreducible character \(\chi\) of \(G\) such that \(H\) is a \(\chi\)-subgroup of \(G\). The author also determines characters \(\chi\) of \(G\) for which \(H\) is not a \(\chi\)-subgroup.