We classify " nice " loop envelopes to Bruck loops of 2-power exponent under the assumption that every nonabelian simple section of G is either passive or isomorphic to PSL2(q), q − 1 ≥ 4 a 2-power. The hypothesis is verified in a separate paper. This paper is a continuation of the work by Aschbacher, Kinyon and Phillips on finite Bruck loops [AKP]. In [BS3] we will apply these results and get ...

Finite groups are of the greatest importance in science. Loops are a simple generalization of finite groups: they share all the group axioms except for the requirement that the binary operation be associative. The least loops that are not themselves groups are those of order five. We offer a brief discussion of these loops and challenge the reader (especially Holger) to find useful applications...

An extremal element in a Lie algebra g over field of characteristic not 2 is an x ∈ such that [ , ] contained the linear span . The element, called point, inner ideal i.e. subspace I satisfying ≤ We show different from 3 geometry with point set points and as lines minimal ideals containing at least two Moufang spherical building, or case there are no set. This last result on sets obtained by co...

K-loops have their origin in the theory of sharply 2-transitive groups. In this paper a proof is given that K-loops and Bruck loops are the same. For the proof it is necessary to show that in a (left) Bruck loop the left inner mappings L(b)L(a)L(ab)−" are automorphisms. This paper generalizes results of Glauberman[3], Kist[8] and Kreuzer[9].

An analysis of the monopole loop length distribution is performed in Wilson-action SU(2) lattice gauge theory. A pure power law in the inverse length is found, at least for loops of length, l, less than the linear lattice size N. This power shows a definite β dependence, passing 5 around β = 2.9, and appears to have very little finite lattice size dependence. It is shown that when this power ex...

We prove that if a root group of a special Moufang set contains an element of order p ≡ 1 (mod 4) then it is abelian.