it was shown in [a. azimifard, e. samei, n. spronk, jfa 256 (2009)] that the zl-amenability constant of a finite group is always at least~$1$, with equality if and only if the group is abelian. it was also shown in [a. azimifard, e. samei, n. spronk, op cit.] that for any finite non-abelian group this invariant is at least $301/300$, but the proof relies crucially on a deep result of d. a. ride...

Motivated by quantum simulation, we consider lattice Hamiltonians for Yang-Mills gauge theories with finite group, example a subgroup of compact Lie group. We show that the electric Hamiltonian admits an interpretation as certain natural, nonunique Laplacian operator on Abelian or non-Abelian group and derive some consequences from this fact. Independent chosen Hamiltonian, provide full explici...

Left braces, introduced by Rump, have turned out to provide an important tool in the study of set-theoretic solutions quantum Yang–Baxter equation. In particular, they allowed construct several new families solutions. A left brace ( B , + ? ) is a structure determined two group structures on set : abelian and satisfying certain compatibility conditions. The main result this paper shows that eve...

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

‎In this paper we prove that a finite group $G$ having at most three‎ ‎conjugacy classes of non-normal non-abelian proper subgroups is‎ ‎always solvable except for $Gcong{rm{A_5}}$‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎non-abelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891--896.]‎. ‎Moreover‎, ‎we s...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...