A sufficient condition for the representation group for a nonabelian representation (Definition 1.1) of a finite partial linear space to be a finite p-group is given (Theorem 2.9). We characterize finite symplectic polar spaces of rank r at least two and of odd prime order p as the only finite polar spaces of rank at least two and of prime order admitting nonabelian representations. The represe...

The spectrum $\omega(G)$ is the set of orders elements $G$. We consider problem generating a finite nonabelian simple group $G$ given by degree if an alternating group, or Lie type, rank and order underlying field type.

We propose a definition of “nonabelian mixed Hodge structure” together with a construction associating to a smooth projective variety X and to a nonabelian mixed Hodge structure V , the “nonabelian cohomology of X with coefficients in V ” which is a (pre-)nonabelian mixed Hodge structure denoted H = Hom(XM , V ). We describe the basic definitions and then give some conjectures saying what is su...

In this paper a rst step in classifying the fuzzy subgroups of a nite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.

We study charge screening in a system of two dimensional nonabelian vortices, at finite temperature. Such vortices are generated after an SO(3) global symmetry group is spontaneously broken to a discrete subgroup Q8, where the latter is isomorphic to the nonabelian group of quaternions. Poisson-Boltzmann like equations are derived for the various inter-vortex potentials, and the solutions to lo...

a longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$‎. ‎let $g$ be a finite nonabelian $p$-group‎. ‎it is known that if $g$ is regular or of nilpotency class $2$ or the commutator subgroup of $g$ is cyclic‎, ‎or $g/z(g)$ is powerful‎, ‎then $g$ has a noninner automorphism of order $p$ leaving either the center $z(g)$ or the frattin...

We investigate the modular properties of the characters which appear in the partition functions of nonabelian fractional quantum Hall states. We first give the annulus partition function for nonabelian FQH states formed by spinon and holon (spinonholon state). The degrees of freedom of spin are described by the SU(2) Kac-Moody algebra at level k. The partition function and the Hilbert space of ...

We introduce a method for obtaining provable polynomial time solutions of problems in nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and more efficient than earlier methods. After demonstrating its applicability to the major classic nonabelian protocols, we use this method to cryptanalyze the Triple Decomposition key exchange protocol, the only classic gro...