The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...

the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}(2^5{:}s_{6})$ of $a(4)$ of index $63$‎.

We extend the analysis [18] of the canonical structure of the Wess-Zumino-Witten theory to the bulk and boundary coset G/H models. The phase spaces of the coset theories in the closed and in the open geometry appear to coincide with those of a double ChernSimons theory on two different 3-manifolds. In particular, we obtain an explicit description of the canonical structure of the boundary G/G c...

Aktract-Construction of efficient block-encoded M-ary phase shift keying (M-PSK) schemes is investigated in this paper. An algebraic approach is adopted in which the basic modulation signals are associated with the elements of a finite group. Using some of the properties of group partition chains, the algebraic properties of linear codes are investigated. From this analysis, a class of codes ca...

We study two group theoretic problems, Group Intersection and Double Coset Membership, in the setting of black-box groups, where Double Coset Membership generalizes a set of problems, including Group Membership, Group Factorization, and Coset Intersection. No polynomial-time classical algorithms are known for these problems. We show that for solvable groups, there exist efficient quantum algori...

Coset enumeration, based on the methods described by Todd & Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such presentation. We show that it is much easier than it rst appears, albeit at the ...

This article presents the examination of the possibility that group Eg' F21 operates on a symmetric design with parameters (133,33,8) as its automorphism group. The method based on coset enumeration in group is used.

We construct smallest known trivalent graphs for girths 16 and 18. One construction uses voltage graphs, and the other coset enumeration techniques for group presentations. AMS Subject Classifications: 05C25, 05C35

After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.

We study the nonunitary diagonal cosets constructed from admissible representations of Kač-Moody algebras at fractional level, with an emphasis on the question of field identification. Generic classes of field identifications are obtained from the analysis of the modular S matrix. These include the usual class related to outer automorphisms, as well as some intrinsically nonunitary field identi...