In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism testing for nonabelian groups. Le Gall has constructed an efficient classical algorithm for a class of groups corresponding to one of the most natural w...

It is proposed that there exist, within a new SU (2) ′ , a gauged discrete group Q 6 (the order 12 double dihedral group) acting as a family symmetry. This nonabelian finite group can explain hierarchical features of families, using an assignment for quarks and leptons dictated by the requirements of anomaly cancellation and of no additional quarks.

In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.

We study model-theoretic and stability-theoretic properties of the nonabelian free group in the light of Sela’s recent result [15] on stability and results announced by Bestvina and Feighn on “negligible subsets” of free groups. We point out analogies between the free group and socalled bad groups of finite Morley rank, and prove “non CM -triviality” of the free group.

There are several reasons to be interested in quantum, nonabelian monopoles. First, if confinement of QCD is a sort of dual superconductor, it is likely to be one of nonabelian variety. Then the effective degrees of freedom involve nonabelian, and not, better understood abelian monopoles. Second, the phenomenon of confinement has to do with fully quantum mechanical, and not semi-classical, beha...

In this paper, we define the vanishing-off subgroup of a nonabelian group. We study the structure of the quotient of this subgroup and a central series obtained from this subgroup. MSC primary: 20C15, MSC secondary: 20D25

We say that finite groups are isospectral if they have the same sets of orders elements. It is known every nonsolvable group $G$ to a simple has unique nonabelian composition factor, is, quotient by solvable radical an almost group. The main goal this paper prove cyclic extension its socle. To end, we consider general situation when arbitrary with not necessarily group, and study prime graph $G...

It is shown how the deformation of the superconformal generators on the string’s worldsheet by a nonabelian super-Wilson line gives rise to a covariant exterior derivative on loop space coming from a nonabelian 2-form on target space. The expression obtained this way is new in the context of strings (but has been considered before in the context of integrable systems), and its consistency is ve...

We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem...

The statement “no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator” 1) is equivalent to the Kervaire–Laudenbach conjecture; 2) becomes true under the additional assumption that the initial nonsimple group is either finite or torsion-free.