— In the present paper, we study the p-adic Teichmüller theory in the case where p = 3. In particular, we discuss nilpotent admissible/ordinary indigenous bundles over a projective smooth curve in characteristic three. The main result of the present paper is a characterization of the supersingular divisors of nilpotent admissible/ordinary indigenous bundles in characteristic three by means of v...

A finite non-abelian group G is called metahamiltonian if every subgroup of either abelian or normal in G. If non-nilpotent, then the structure has been determined. nilpotent, determined by its Sylow subgroups. However, classification p-groups an unsolved problem. In this paper, are completely classified up to isomorphism.

Let G be a reductive group scheme over the p-adic integers, and let $$\mu $$ minuscule cocharacter for G. In Hodge-type case, we construct functor from nilpotent $$(G,\mu )$$ -displays p-nilpotent rings R to formal p-divisible groups equipped with crystalline Tate tensors. When R/pR has p-basis étale locally, show that this defines an equivalence between two categories. The definition of relies...

In this paper a large family of dominant Fitting classes of finite soluble groups and the description of the corresponding injectors are obtained. Classical constructions of nilpotent and Lockett injectors as well as p-nilpotent injectors arise as particular cases. 1994 Mathematics subject classification (Amer. Math. Soc.): primary 20D10.

We adapt the p-group generation algorithm to classify small-dimensional nilpotent Lie algebras over small fields. Using an implementation of this algorithm, we list the nilpotent Lie algebras of dimension at most 9 over F2 and those of dimension at most 7 over F3 and F5 .

Abstract. Fix a field F. A zero-nonzero pattern A is said to be potentially nilpotent over F if there exists a matrix with entries in F with zero-nonzero pattern A that allows nilpotence. In this paper we initiate an investigation into which zero-nonzero patterns are potentially nilpotent over F, with a special emphasis on the case that F = Zp is a finite field. As part of this investigation, w...

Conditions are given for a class 2 nilpotent group to have no central extensions of class 3. This is related to Betti numbers and to the problem of representing a class 2 nilpotent group as the fundamental group of a smooth projective variety. Surveys of the work on the characterization of the fundamental groups of smooth projective varieties and Kähler manifolds (see [1],[3], [9]) indicate tha...

It is shown that projectivized irreducible components of nilpotent cones of complex symmetric spaces are projective self-dual algebraic varieties. Other properties equivalent to their projective self-duality are found. 1. Let g be a semisimple complex Lie algebra, let G be the adjoint group of g, and let θ ∈ Aut g be an element of order 2. We set k := {x ∈ g | θ(x) = x}, p := {x ∈ g | θ(x) = −x...