CHARACTERISTIC FUZZY GROUPS

ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

Stably Cayley Groups in Characteristic

A linear algebraic group G over a field k is called a Cayley group if it admits a Cayley map, i.e., a G-equivariant birational isomorphism over k between the group variety G and its Lie algebra. A Cayley map can be thought of as a partial algebraic analogue of the exponential map. A prototypical example is the classical “Cayley transform” for the special orthogonal group SOn defined by Arthur C...

Alternating groups as monodromy groups in positive characteristic

Let X be a generic curve of genus g defined over an algebraically closed field k of characteristic p ≥ 0. We show that for n sufficiently large there exists a tame rational map f : X → P1k with monodromy group An. This generalizes a result of Magaard–Völklein to positive characteristic.

Non-Commutative Formal Groups in Positive Characteristic

We describe geometric non-commutative formal groups in terms of a geometric commutative formal group with a Poisson structure on its splay algebra. We describe certain natural properties of such Poisson structures and show that any such Poisson structure gives rise to a non-commutative formal group. We describe geometric non-commutative formal groups in terms of a geometric commutative formal g...

Topology of Lie Groups and Characteristic Classes