We study finite groups G with the property that for any subgroup M maximal in whose order is divisible by all prime divisors of |G|, supersolvable. show nonabelian simple group can occur as a composition factor such and that, if solvable, then nilpotency length rank are arbitrarily large. On other hand, every p, p-length at most 1. This answers questions proposed V. Monakhov The Kourovka Notebo...

We show that the ‘standard’ quantum algorithm for the abelian hidden subgroup problem is not only efficient but is optimal in the information theoretic sense, in that it maximizes the probability of correctly identifying the hidden subgroup. The proof uses semidefinite programming to show that the standard algorithm implements the optimal set of measurements. The arguments break down for the no...

In the present talk we present an investigation of nonabelian SU(N) gauge theories, describing a system of fields with non–dual g and dual g̃ charges and revealing the generalized dual symmetry. The Zwanziger type action is suggested. The renormalization group equations for pure nonabelian theories, in particular for pure SU(3) × S̃U(3) gauge theory (as an example) are analysed. We consider not o...

We prove that the fundamental group of the space of the real points of M0,n(C) is nonabelian (Theorem 14). The technique has a topological nature. Also, we prove that these spaces are non-orientable manifolds (Theorem 16). To our knowledge, the results are new.In a forthcoming manuscript, we investigate the associated combinatorial structures. Many of them were already studied in Computational ...

We study the WZNW models based on nonstandard bilinear forms. We approach the problem from algebraic, perturbative and functional exact methods. It is shown that even in the case of integer k we can find irrational CFT’s. We prove that when the base group is noncompact with nonabelian maximal compact subgroup, the KacMoody representations are nonunitary.

Fortysix mutually nonisomorphic symmetric (64,28,12)-designs have been constructed by means of tactical decompositions. They all admit an action of the nonabelian group of order 21. The computation of their full automorphism groups as well as their derived (28,12,11)-designs proves that none of them can be isomorphic to any of the known (64,28,12)-designs.

In this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a nonabelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1463 non-isomorphic designs. The orders of the full automorphism groups of these designs all...

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph that determines which case holds. We also consider some examples of solvable subgroups, including one that is not virtually nilpotent and is embedded in a no...

This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus the concept a positive definite function group and our primary goal is to understand how such functions can be extended from balls finite radius entire group. Previous work showed that extensions always exist we study problem simultaneous extension multiple functions. More specifically, define ‘relative ...

The new generalization of the gauge interaction for the bosonic strings is found. We consider some quasi-equivariant maps from the space of metrics on the worldsheet to the space of n-tuples of oneand two-dimensional loops. The two-dimensional case is based on the cylinders interacted with a path space connection. The special 2-gauge string model is formulated using two 1-connections, nonabelia...