2-group symmetries arise when 1-form and 0-form of a theory mix with each other under group multiplication. We discover the existence in 5d N=1 abelian gauge theories arising on (non-extended) Coulomb branch superconformal field (SCFTs), leading us to argue that UV SCFT itself admits symmetry. Furthermore, our analysis determines global forms flavor symmetry groups SCFTs, irrespective whether o...

In this paper, we propose a brand new public key encryption scheme in the Lie group that is a non-abelian group. In particular, we firstly investigate the intractability assumptions in the Lie group, including the non-abelian factoring assumption and non-abelian inserting assumption. After that, by using the FO technique, a CCA secure public key encryption scheme in the Lie group is proposed. A...

For given non-abelian group G, the non-commuting (NC)-graph $Gamma(G)$ is a graph with the vertex set $G$ $Z(G)$ and two distinct vertices $x, yin V(Gamma)$ are adjacent whenever $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of simple modules subcharacter algebra finite group. abelian groups, prove deformation given by inclusion natural numbers, which corresponds to generated fibred bisets over field characteristic zero, is not semisimple. In cyclic group prime order case, provide complete description semisimple deform...

A group homomorphism η : A → H is called a localization of A if every homomorphism φ : A→ H can be ‘extended uniquely’ to a homomorphism Φ : H → H in the sense that Φη = φ. This categorical concept, obviously not depending on the notion of groups, extends classical localizations as known for rings and modules. Moreover this setting has interesting applications in homotopy theory, see the introd...

A group homomorphism η : A → H is called a localization of A if every homomorphism φ : A → H can be ‘extended uniquely’ to a homomorphism Φ : H → H in the sense that Φη = φ. This categorical concepts, obviously not depending on the notion of groups, extends classical localizations as known for rings and modules. Moreover this setting has interesting applications in homotopy theory, see the intr...

This paper is motivated by R. H. Bruck’s paper[3], in which he proved that the existence of cyclic projective plane of order n ≡ 1 (mod 3) implies that of a non-planar difference set of the same order by proving that such a cyclic projective plane admits a regular non-Abelian automorphism group using n as a multiplier. In this paper we will discuss in detail the possibility of using multipliers...

Let Π be a finite projective plane admitting a large abelian collineation group. It is well known that this situation may be studied by algebraic means (via a representation by suitable types of difference sets), namely using group rings and algebraic number theory and leading to rather strong nonexistence results. What is less well-known is the fact that the abelian group (and sometimes its gr...