On LCA groups each of whose characters is ultimately measurable

On Groups whose Geodesic Growth is Polynomial

This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set with respect to which the geodesic growt...

Measure zero sets whose algebraic sum is non - measurable

In this note we will show that for every natural number n > 0 there exists an S ⊂ [0, 1] such that its n-th algebraic sum nS = S + · · ·+ S is a nowhere dense measure zero set, but its n+1-st algebraic sum nS+S is neither measurable nor it has the Baire property. In addition, the set S will be also a Hamel base, that is, a linear base of R over Q. We use the standard notation as in [2]. Thus sy...

Groups whose set of vanishing elements is exactly a conjugacy class

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

On characters of Weyl groups

In this note a combinatorial character formula related to the symmetric group is generalized to an arbitrary finite Weyl group. 1 The Case of the Symmetric Group The length l(π) of a permutation π ∈ Sn is the number of inversions of π, i.e., the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). For any permutation π ∈ Sn let m(π) be defined as (1) m(π) := 

φ-factorable operators and Weyl-Heisenberg frames on LCA groups