Nonabelian magnetic monopoles of Goddard-Nuyts-Olive-Weinberg type have recently been shown to appear as the dominant infrared degrees of freedom in a class of softly broken N = 2 supersymmetric gauge theories in which the gauge group G is broken to various nonabelian subgroups H by an adjoint Higgs VEV. When the low-energy gauge group H is further broken completely by e.g. squark VEVs, the mon...

We report some results on deterministic algorithms for efficient management of matrix groups over finite fields. Our results generalize Luks’s work on solvable matrix groups to wider classes of matrix groups. In this article, we present algorithms for membership-testing and its closely related problems. The algorithms run deterministically in time polynomial in these three parameters: the input...

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As an application, the duality breaking for group bundles vs. tensor C*-categories with non-simple unit is discussed in the setting of Nistor-Troitsky gauge-eq...

A group G has a Frobenius graphical representation (GFR) if there is simple graph ? whose full automorphism isomorphic to acting on the vertices as group. In particular, any with GFR and Cayley graph. By very recent results of Spiga, exists function f such that finite complement H | > (| |) then admits GFR. This paper provides an infinite family graphs admit GFRs despite not meeting Spiga’s ...

A theorem of Cantat and Urech says that an analog the classical Tits alternative holds for group birational automorphisms a compact complex Kaehler surface. We established in our previous paper following Tits-type alternative: if X is toric affine variety G subgroup Aut(X) generated by finite set unipotent subgroups normalized acting torus then either contains nonabelian free or algebraic group...

Let G be a finite nonabelian group. We show how an endomorphism of with abelian image gives rise to family binary operations {?n:n?Z?0} on such that (G,?m,?n) is skew left brace for all m,n?0. A block number non-degenerate set-theoretic solutions the Yang-Baxter equation. give examples showing obtained can arbitrarily large.

Let G be a finite group and let $GK(G)$ be the prime graph of G. We assume that $n$ is an odd number. In this paper, we show that if $GK(G)=GK(B_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then G has a unique nonabelian composition factor isomorphic to $B_n(p)$ or $C_n(p)$ . As consequences of our result, $B_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the ...

A charge operator is constructed for a quantum field theory with an abelian discrete gauge symmetry, and a non-local order parameter is formulated that specifies how the gauge symmetry is realized. If the discrete gauge symmetry is manifest, then the charge inside a large region can be detected at the boundary of the region, even in a theory with no massless gauge fields. This long-range effect...

In this paper we find the complete structure for the automorphism groups of metacyclic minimal nonabelian 2-groups. This, together with [6, 7], gives the complete answer to the Question 15 from [5] (respectively Question 20 from [4]) in the case of metacyclic groups. We also correct some inaccuracies and extend the results from [13].