The number of lifts of a Brauer character with a normal vertex.
Let \(p\) be a prime, let \(G\) be a \(p\)-solvable group, and let \(\varphi\) be an irreducible \(p\)-modular character of \(G\). By a theorem of Fong and Swan, there exists an ordinary irreducible character \(\chi\) of \(G\) such that the restriction of \(\chi\) to the \(p\)-regular conjugacy classes of \(G\) is equal to \(\varphi\). In this case, \(\chi\) is called a lift of \(\varphi\). The main result of the paper is that if the vertex \(Q\) of \(\varphi\) is normal in \(G\) and either \(p\) is odd or \(Q\) is Abelian, then the number of lifts of \(\varphi\) is bounded above by the index \([Q:Q']\). In particular, if \(Q\) is Abelian the number of lifts of \(\varphi\) is at most \(|Q|\).
scientific article; zbMATH DE number 5888505
scientific article