Let G be a finite group and let T1 denote the number of times a triple (x, y, z) ∈ G3 binds X, where X = {xyz, xzy, yxz, yzx, zxy, zyx}, to one conjugacy class. Let T2 denote the number of times a triple in G3 breaks X into two conjugacy classes. We have established the following results: i) the probability that a triple (x, y, z) ∈ D3 n binds X to one conjugacy class is ≥ 58 . ii) for groups s...

We introduce a generalized Anshel-Anshel-Goldfeld (AAG) key establishment protocol (KEP) for magmas. This leads to the foundation of non-associative public-key cryptography (PKC), generalizing the concept of non-commutative PKC. We show that left selfdistributive systems appear in a natural special case of a generalized AAG-KEP for magmas, and we propose, among others instances, concrete realiz...

Several decades ago, John McKay suggested a correspondence between nodes of the affine E8 Dynkin diagram and certain conjugacy classes in the Monster group. Thanks to Monstrous Moonshine, this correspondence can be recast as an assignment of discrete subgroups of PSL2(R) to nodes of the affine E8 Dynkin diagram. The purpose of this article is to give an explanation for this latter correspondenc...

Suppose $G$ is a connected complex semisimple group and $W$ its Weyl group. The lifting of an element to semisimple. This induces well-defined map from the set elliptic conjugacy classes $G$. In this paper, we give uniform algorithm compute map. We also consider twisted case.

We first examine Howard's analysis of the Bell factorizability condition in terms of 'separability' and 'locality' and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of 'non-separability' rather than 'non-locality' and that 'non-separability' implies the failure of space-time as a principle of ...

In this paper, we propose a fast combined separability filter, which can selectively detect circular features such as pupils and nostrils in an image of the human face. The proposed filter is designed as a combination of multiple rectangle separability filters so that it can achieve high-speed processing and high positioning accuracy at the same time. The evaluation experiments using synthetic ...

In machine learning, the performance of a classifier depends on both model and separability/complexity datasets. To quantitatively measure separability datasets, in this study, we propose an intrinsic – Distance-based Separability Index (DSI), which is independent model. We then formally show that DSI can indicate whether distributions datasets are identical for any dimensionality. because cons...

We define a Rohlin property for Z-actions on UHF algebras and show a non-commutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. We consider two classes of UHF algebras. For UHF algebras in one class including the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebra...

We provide the first effectively computable, modulo a mild conjecture, complete invariant for simultaneous conjugacy in Garside groups. This invariant generalizes the notion of super summit set of a conjugacy class, and provides a solution of the simultaneous conjugacy problem in Garside groups, of complexity a small degree polynomial in the sizes of the invariant and the input parameters. Comp...

Subgroups H1 and H2 of a group G are said to be locally conjugate if there is a bijection f : H1 → H2 such that h and f(h) are conjugate in G. We study local conjugacy among subgroups of GL2(Z/pZ), where p is an odd prime, building on Andrew Sutherland’s categorizations of subgroups of GL2(Z/pZ) and local conjugacy among them. We obtain a classification of locally conjugate subgroups of GL2(Z/p...