The blocks of p-nilpotent groups over arbitrary fields

Nilpotent Primitive Linear Groups over Finite Fields

In this paper we investigate the structure of groups as in the title. Our work builds on work of several other authors, namely Konyuh [5], Leedham-Green and Plesken [6], and Zalesskii [10], who have described the abstract isomorphism types of the groups. We obtain more detailed descriptions, in particular explaining how group structure depends on the existence of an abelian primitive subgroup. ...

Algebraic Groups over Arbitrary Fields

In this chapter, we study algebraic groups, especially nonsplit reductive groups, over arbitrary fields. The algebraic groups over a field k that become isomorphic to a fixed algebraic group over kal are classified by a certain cohomology group. In the first section, we explain this, and discuss what is known about the cohomology groups. Over an algebraically closed field, the classical semisim...

Calculating Invariant Rings of Finite Groups over Arbitrary Fields

If G is a finite linear group over a field K such that char(K) | 6 |G|, there are various effective methods to calculate the invariant ring I of G, i.e., to find a finite system of generators of I as an algebra over K (see Sturmfels, 1993, Section 2; McShane, 1992; Kemper, 1993, 1994). These methods make use of the Reynolds operator, Molien’s formula, the Cohen–Macaulay property of invariant ri...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

NILPOTENT p-LOCAL FINITE GROUPS

In this paper we provide characterizations of p-nilpotency for fusion systems and p-local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.