Thep-Intersection Subgroups in Quasi-Simple and Almost Simple Finite Groups

AbstractLetpbe a fixed prime andGa finite group. A proper subgroupX<Gis called ap-intersection subgroupifX∩Xgis ap-group for eachg∈G\X, butXis not ap-group. In this paper we classify thep-intersection subgroups in the quasi-simple and almost simple finite groups

The character table of a split extension of the Heisenberg group H1(q)H_1(q) by Sp(2,q)Sp(2,q), qq odd

In this paper we determine the full character table of a certain split extension $H_1(q)\rtimes Sp(2,q)$ of the Heisenberg group $H_1$ by the odd-characteristic symplectic group $Sp(2,q)$.Comment: 9 page

The structure of blocks with a Klein four defect group

We prove Erdmann’s conjecture [16] stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig’s finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups