Let G1 × G2 be a subgroup of SO3(R) such that the two factors G1 and G2 are non-trivial groups. We show that if G1 × G2 is not abelian, then one factor is the (abelian) group of order 2, and the other factor is nonabelian and contains an element of order 2. There exist finite and infinite such non-abelian subgroups. Let F2 be the free group of rank 2. It is well-known that the group SO3(R) has ...

the non commuting graph of a non-abelian finite group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we prove some new results about this graph. in particular we will give a new proof of theorem 3.24 of [2]. we also prove that if $g_1$, $g_2$, ..., $...

The existence of nonsingular classical magnetic monopole solutions is usually understood in terms of topologically nontrivial Higgs field configurations. We show that finite energy magnetic monopole solutions also exist within a class of purely Abelian gauge theories containing charged vector mesons, even though the possibility of nontrivial topology does not even arise. provided that certain r...

We prove that if a countable group is elementarily equivalent to non-abelian free and all of its abelian subgroups are cyclic, then the union chain regular NTQ groups (i.e., hyperbolic towers).

Non-Abelian plasma instabilities may be responsible for the fast apparent quark-gluon thermalization in relativistic heavy-ion collisions if their exponential growth is not hindered by nonlinearities. We study numerically the real-time evolution of instabilities in an anisotropic non-Abelian plasma with an SU(2) gauge group in the hard-loop approximation. We find exponential growth of non-Abeli...

We present a new link invariant which depends on a representation of the link group in SO(3). The computer calculations indicate that an abelian version of this invariant is expressed in terms of the Alexander polynomial of the link. On the other hand, if we use non abelian representation, we get the squared non abelian Reidemeister torsion (at least for some torus knots). Introduction In this ...

In this letter we reconsider the role of Lorentz invariance in the dynami-cal generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. Remarkably, the application of this principle to the most general rel...