Regular orbits of linear groups
The author shows the following well-known theorem: Let \(p\) be a prime with \(p>5^{30}\). Suppose that \(G\) is a \(p'\)-group and \(V\) is a faithful \(\mathbb{F}_pG\)-module such that \(G\) has a quasi-simple normal subgroup \(H\) which is irreducible on \(V\). Then one of the following holds: (i) \(G\) has a regular orbit on the vectors of \(V\); (ii) \(H=A_c\), \(c<p\), and \(V\) is the ``natural'' module for \(H\).
scientific article; zbMATH DE number 941284