Hegyvári and Hennecart showed that if B is a sufficiently large brick of a Heisenberg group, then the product set B ·B contains many cosets of the center of the group. We give a new, robust proof of this theorem that extends to all extra special groups as well as to a large family of quasigroups.

We prove that the near hexagon Q(5,2)× L3 has a non-abelian representation in the extra-special 2-group 21+12 + and that the near hexagon Q(5,2)⊗Q(5,2) has a non-abelian representation in the extra-special 2-group 21+18 − . The description of the non-abelian representation of Q(5,2)⊗Q(5,2) makes use of a new combinatorial construction of this near hexagon.

With the ansatz that there exist local or global discrete symmetries in the special branes’ neighborhoods, we can construct the extra dimension models with only zero modes, or the models which have large extra dimensions and arbitrarily heavy KK modes because there is no simple relation between the mass scales of extra dimensions and the masses of KK states. In addition, the bulk gauge symmetry...

Let p a be prime number. Using algebraic methods from the factorization theory of abelian groups we will prove a result about the structure of the 1-error correcting t-shift integer codes over the alphabet Zp in the special case when t is a prime. The algorithms to construct such codes can take advantage of this extra structural information in a straightforward manner and the search for these c...

We show that every rank two p-group acts freely and smoothly on a product of two spheres. This follows from a more general construction: given a smooth action of a finite group G on a manifold M , we construct a smooth free action on M×S1×· · ·×Sk when the set of isotropy subgroups of the G-action on M can be associated to a fusion system satisfying certain properties. Another consequence of th...

In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class C of 2-Engel 3-groups of exponent 27 and under this correspondance we will see that the nilpotent algebras corre...

BACKGROUND 18F-FDG PET has been used in sarcoidosis for diagnosis and determination of the extent of the disease. However, assessing inflammatory lesions in cardiac sarcoidosis using 18F-FDG can be challenging because it accumulates physiologically in normal myocardium. Another radiotracer, 3'-deoxy-3'-18F-fluorothymidine (18F-FLT), has been investigated as a promising PET tracer for evaluating...