The \(p\)-intersection subgroups in quasi-simple and almost simple finite groups
Let \(G\) be a finite group and \(p\) a prime number. A subgroup \(X\) is called a \(p\)-intersection group if \(X\cap X^g\) is a \(p\)-group for \(g\in G-X\), but \(X\) is not a \(p\)-group. In the paper under review all \(p\)-intersection groups \(X\) are determined when \(G\) is a quasi-simple or almost simple group. For the long list of such pairs \((G,X)\) we refer the reader to the paper itself. The authors of this article apply this result and classify [in Proc. Am. Math. Soc. 126, No. 5, 1337-1343 (1998; Zbl 0897.20003)] all primitive permutation groups in which a two-point stabilizer is a \(p\)-group.
scientific article; zbMATH DE number 1213845