Suppose (X,σ) is a subshift, PX(n) is the word complexity function of X, and Aut(X) is the group of automorphisms of X. We show that if PX(n) = o(n 2/ log n), then Aut(X) is amenable (as a countable, discrete group). We further show that if PX(n) = o(n 2), then Aut(X) can never contain a nonabelian free semigroup (and, in particular, can never contain a nonabelian free subgroup). This is in con...

We construct a new compactification of a noncompact rank one globally symmetric space. The result is a nonmetrizable space which also compactifies the Borel–Serre enlargement X of X , contractible only in the appropriate Čech sense, and with the action of any arithmetic subgroup of the isometry group of X on X not being small at infinity. Nevertheless, we show that such a compactification can b...

Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. We study Fourier transforms of compactly supported K-finite distributions on X and characterize the image of the space of such distributions.

The discrete subgroup ∆(27) of SU(3) has the interesting multiplication rule 3×3 = 3̄ + 3̄ + 3̄, which is used to obtain near tribimaximal neutrino mixing. Using present neutrino oscillation data as input, this model predicts that the effective mass mee measured in neutrinoless double beta decay will be 0.14 eV. The non-Abelian discrete subgroup ∆(12) of SU(3) [1], more familiarly known as A4 [2, ...

Let AutKK(x) be the Galois group of the transcendental degree one pure field extension K ⊆ K(x). In this paper we describe polynomial time algorithms for computing the field Fix(H) fixed by a subgroup H ⊆ AutKK(x) and for computing the fixing group Gf of a rational function f ∈ K(x).

Let G be a closed subgroup of S∞ and X be a Polish G-space with a countable basisA of clopen sets. Each x ∈ X defines a characteristic function τx on A by τx(A) = 1 ⇔ x ∈ A. We consider computable complexity of τx and some related questions.

Suppose n is a fixed positive integer. We introduce the relative n-th non-commuting graph ΓH,G, associated to the nonabelian subgroup H of group G. The vertex set is G \ C H,G in which C H,G = {x ∈ G : [x, y] = 1 and [x, y] = 1 for all y ∈ H}. Moreover, {x, y} is an edge if x or y belong to H and xy 6= yx or xy 6= yx. In fact, the relative n-th commutativity degree, Pn(H,G) the probability that...

We extend Kovacic’s algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions could be found, we give a necessary and sufficient condition for the integrability of the system. We give various examples of computation. Introduction Let us consider the linear differential equation ( ∂XY (X) ∂2 XY (...

In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.

 ‎Let $tilde{F}=(Q,S,tilde{R},Z,omega,tilde{delta},‎ F_1,F_2)$‎ ‎be a general fuzzy automaton and the set of its states be a group.‎ ‎The aim of this paper is the study of applications of a group in a‎ ‎general fuzzy automaton‎. ‎For this purpose‎, ‎we define the concepts‎ ‎of fuzzy normal kernel of a general fuzzy automaton‎, ‎fuzzy kernel‎ ‎of a general fuzzy automaton‎, ‎adjustable‎, ‎multip...