Related papers: Lee metrics on groups

We use the theory of blocks of cyclic defect to prove that under a certain condition on the principal p-block of a finite group G the normalized unit group of the integral group ring of G contains an element of order pq if and only if so…

In this paper, we generalize the notion of cyclic metric to homogeneous Finsler geometry. Firstly, we prove that a homogeneous Finsler space $(G/H, F)$ must be symmetric when it satisfies the naturally reductive and cyclic conditions…

Data sets sampled in Lie groups are widespread, and as with multivariate data, it is important for many applications to assess the differences between the sets in terms of their distributions. Indices for this task are usually derived by…

We associate a graph $\Gamma_G$ to a non locally cyclic group $G$ (called the non-cyclic graph of $G$) as follows: take $G\backslash Cyc(G)$ as vertex set, where $Cyc(G)=\{x\in G | \left<x,y\right> \text{is cyclic for all} y\in G\}$, and…

The characterization of distance-regular Cayley graphs originated from the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets. In this paper, a classification of distance-regular Cayley…

An $integral$ of a group $G$ is a group $H$ whose derived group (commutator subgroup) is isomorphic to $G$. This paper discusses integrals of groups, and in particular questions about which groups have integrals and how big or small those…

Let N be a nilpotent Lie group and let S be an invariant geometric structure on N (cf. symplectic, complex or hypercomplex). We define a left invariant Riemannian metric on N compatible with S to be "minimal", if it minimizes the norm of…

If $G$ is a compact Lie group endowed with a left invariant metric $g$, then $G$ acts via pullback by isometries on each eigenspace of the associated Laplace operator $\Delta_g$. We establish algebraic criteria for the existence of left…

For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is…

Let (N,g) be a nilpotent Lie group endowed with an invariant geometric structure (cf. symplectic, complex, hypercomplex or any of their `almost' versions). We define a left invariant Riemannian metric on N compatible with g to be minimal,…

We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricci-parallel. We show the same result for any Lie group of dimension $\leq$ 6.

With a f-left-invariant Riemannian metric on a Lie group $G$, we mean a Riemannian metric which is conformally equivalent to a left-invariant Riemannian metric, with the conformal factor $f$. In this article, we study the geometry of such…

In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…

We prove that if $H$ is a subgroup of index $n$ of any cyclic group $G$, then $G$ can be isometrically embedded in $(H^n, d_{_{Ham}}^n)$, thus generalizing previous results of Carlet (1998) for $G=\mathbb{Z}_{2^k}$ and Yildiz-\"Ozger (2012)…

The fundamental inequality of Guivarc'h relates the entropy and the drift of random walks on groups. It is strict if and only if the random walk does not behave like the uniform measure on balls. We prove that, in any nonelementary…

In this paper, we classify three-locally-symmetric spaces for a connected, compact and simple Lie group. Furthermore, we give the classification of invariant Einstein metrics on these spaces.

We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic…

We study G-invariant Kaehler metrics on G^C from the Hamiltonian point of view. As an application we show that there exist (GxG)-invariant Ricci-flat Kaehler metrics on G^C for any compact semisimple Lie group G.

We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs $ (G,\mathcal{M}) $, such that $ G $ is a finite 2-group and $ \mathcal{M}…

A finite group $G$ is called Cayley integral if all undirected Cayley graphs over $G$ are integral, i.e., all eigenvalues of the graphs are integers. The Cayley integral groups have been determined by Kloster and Sander in the abelian case,…