Rings associated to coverings of finite $p$-groups

Finite Groups with p-Sylow Coverings

finite groups with p-sylow coverings

Finite subnormal coverings of certain solvable groups

A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...

Rings of Invariants of Finite Groups

We shall prove the fundamental results of Hilbert and Noether for invariant subrings of finite subgroups of the general linear groups in the non-modular case, i.e. when the field has characteristic zero or coprime with the order of the group. We will also derive the Molien’s formula for the Hilbert series of the ring of invariants. We will show, through examples, that the Molien’s formula helps...

Representations of Reductive Groups over Finite Rings

In this paper we construct a family of irreducible representations of a Chevalley group over a finite ring R of truncated power series over a field Fq . This is done by a cohomological method extending that of Deligne and the author in the case R = Fq .