— We study the structure of abelian subgroups of Galois groups of function fields.

A three-dimensional polynomial algebra of order m is defined by the commutation relations [P0, P±] = ±P±, [P+, P−] = φ (P0) where φ(P0) is an m-th order polynomial in P0 with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders l and m can be combined to give two distinct (l + m + 1)-th order polynomial ...

There exists a large class of groups of operators acting on Hilbert spaces, where commutativity of group elements can be expressed in the geometric language of symplectic polar spaces embedded in the projective spaces PG(n, p), n being odd and p a prime. Here, we present a result about commuting and non-commuting group elements based on the existence of socalled Möbius pairs of n-simplices, i. ...

in this paper we introduce the construction of free profinite products of profinite groups withcommuting subgroups. we study a particular case: the proper free profinite products of profinite groups with commuting subgroups. we prove some conditions for a free profinite product of profinite groups with commuting subgroups to be proper. we derive some consequences. we also compute profinite comp...

For a group G and X a subset of G the commuting graph of G on X, denoted by C(G,X), is the graph whose vertex set is X with x, y ∈ X joined by an edge if x 6= y and x and y commute. If the elements in X are involutions, then C(G,X) is called a commuting involution graph. This paper studies C(G,X) when G is a 3-dimensional projective special unitary group and X a G-conjugacy class of involutions...

We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the clas...

We prove that for any nonperiodic set of words F ⊆ Σ with at most three elements, the centralizer of F , i.e., the largest set commuting with F , is F ∗. Moreover, any set X commuting with F is of the form X = F I , for some I ⊆ N. A boundary point is thus established, as these results do not hold for all languages with at least four words. This solves a conjecture of Karhumäki and Petre, 2000,...

We prove the `p-spectral radius formula for n-tuples of commuting Banach algebra elements. This generalizes results of [6], [7] and [10]. Let A be a Banach algebra with the unit element denoted by 1. Let a = (a1, . . . , an) be an n-tuple of elements of A. Denote by σ(a) the Harte spectrum of a, i.e. λ = (λ1, . . . , λn) / ∈ σ(a) if and only if there exist u1, . . . , un, v1, . . . , vn ∈ A suc...