Let K be field of characteristic 2 and let G be a finite nonabelian 2-group with the cyclic derived subgroup G′, and there exists a central element z of order 2 in Z(G)\G′. We prove that the unit group of the group algebra KG possesses a section isomorphic to the wreath product of a group of order 2 with the derived subgroup of the group G, giving for such groups a positive answer to the questi...

A remarkable feature of D-branes is the appearance of a nonabelian gauge theory in the description of several (nearly) coincident branes. This nonabelian structure plays an important role in realizing various geometric effects with D-branes. In particular, the branes’ transverse displacements are described by matrix-valued scalar fields and so noncommutative geometry naturally appears in this f...

The notion of amenability was introduced in 1929 by J. von Neumann [68] in order to explain the Banach-Tarski paradox. A countable discrete group Γ is amenable if there exists a left-invariant mean φ : `∞(Γ) → C. The class of amenable groups is stable under subgroups, direct limits, quotients and the free group F2 on two generators is not amenable. Knowing whether or not the class of amenable g...

The validity of Freedman’s disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension 4. Recently, Krushkal and Lee proved a surprising result that surgery theory works for a large special class of 4-manifolds with free nonabelian fundamental groups. The goa...

In developing a model for predicting the nonabelian gauge coupling constants we argue for the phenomenological validity of a “principle of multiple point criticality”. This is supplemented with the assumption of an “(grand) anti-unified” gauge group SMGgen. ∼ U(1)gen. ×SU(2)Ngen. ×SU(3)Ngen. that, at the Planck scale, breaks down to the diagonal subgroup. Here Ngen is the number of generations ...

We first reobtain in a simpler way the Haldane fractional statistics at thermal equilibrium using an interpolation argument. We then show that the mean occupation number for fractional statistics is invariant to a group of duality transformations, a nonabelian subgroup of fractional linear group.

A number of authors have studied the question when a graph can be represented as Cayley on more than one nonisomorphic group. The work to date has focussed few special situations: groups are $p$-groups; order $pq$; graphs normal; or both abelian. In this paper, we construct two infinite families graphs, each which is an abelian group and nonabelian These include smallest examples such that had ...

The properties of BPS monopoles carrying nonabelian magnetic charges are investigated by following the behavior of the moduli space of solutions as the Higgs field is varied from a value giving a purely abelian symmetry breaking to one that leaves a nonabelian subgroup of the gauge symmetry unbroken. As the limit of nonabelian unbroken symmetry is reached, some of the fundamental abelian monopo...

The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension four. Recently, Krushkal and Lee proved a surprising result that surgery theory works for a large special class of 4-manifolds with free nonabelian fundamental groups. The ...

Abstract. Let K be a field of characteristic p and G a nonabelian metacyclic finite p-group. We give an explicit list of all metacyclic p-groups G, such that the group algebra KG over a field of characteristic p has a filtered multiplicative K-basis. We also present an example of a non-metacyclic 2-group G, such that the group algebra KG over any field of characteristic 2 has a filtered multipl...