The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T.Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E....

We prove Timmesfeld’s conjecture that special abstract rank one groups are quasisimple. We show that in a special Moufang set the root groups are characterized on the one hand by being regular and normal in the point stabilizer, and on the other hand a normal transitive nilpotent subgroup of the point stabilizer is a root group. We prove that if a root group of a special Moufang set contains an...

In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.

The abelian-projected monopole loop distribution is extracted from maximal abelian gauge simulations. The number of loops of a given length falls as a power nearly independent of lattice size. This power increases with β = 4/g, reaching five around β = 2.85, beyond which loops any finite fraction of the lattice size vanish in the infinite lattice limit, suggesting the continuum theory lacks con...

The Sylow theorems hold for finite extra loops, as does P. Hall’s theorem for finite solvable extra loops. Every finite nonassociative extra loop Q has a nontrivial center, Z(Q). Furthermore, Q/Z(Q) is a group whenever |Q| < 512. Loop extensions are used to construct an infinite nonassociative extra loop with a trivial center and a nonassociative extra loop Q of order 512 such that Q/Z(Q) is no...