A finite non-abelian group G is called metahamiltonian if every subgroup of either abelian or normal in G. If non-nilpotent, then the structure has been determined. nilpotent, determined by its Sylow subgroups. However, classification p-groups an unsolved problem. In this paper, are completely classified up to isomorphism.

The Hamiltonians of SU(2) and SU(3) gauge theories in 3+1 dimensions can be expressed in terms of gauge invariant spatial geometric variables, i.e., metrics, connections and curvature tensors which are simple local functions of the non-Abelian electric field. The transformed Hamiltonians are local. New results from the same procedure applied to the SU(2) gauge theory in 2+1 dimensions are also ...

We develop the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus three. The specific example of the “purely trigonal”curve y = x +λ3x 3 +λ2x 2 +λ1x+λ0 is discussed in detail, including a list of the associated partial differential equations satisfied by the ℘ functions, and the derivation of two addition formulae.

Sets with a self-distributive operation (in the sense of ( ◃ b ) c = ), in particular quandles, appear knot and braid theories, Hopf algebra classification, study Yang–Baxter equation, other areas. An important invariant quandles is their structure group. The group finite quandle known to be either “boring” (free abelian), or “interesting” (non-abelian torsion). In this paper we explicitly desc...

We discuss general properties and possible types of magnetic vortices in non-Abelian gauge theories (we consider here G = SU(N), SO(N), USp(2N)) in the Higgs phase. The sources of such vortices carry “fractional” quantum numbers such as Zn charge (for SU(N)), but also full non-Abelian charges of the dual gauge group. If such a model is re-interpreted as an effective dual magnetic theory of the ...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...