An absolute ideal of an Abelian group G is a subgroup that in every ring whose additive coincides with G. We describe reduced algebraically compact groups admit at least one structure R such (Problem 93 L. Fuchs’ book “Infinite Groups”). Reduced, compact, have only fully invariant subgroups as are characterized.

The cogrowth of a subgroup is defined as the growth of a set of coset representatives which are of minimal length. A subgroup is essential if it intersects non-trivially every non-trivial subgroup. The main result of this paper is that every function f : N ∪ {0}−→N which is strictly increasing, but at most exponential, is equivalent to a cogrowth function of an essential subgroup of infinite in...

Let lbe a prime, andH a curve of genus 2 over a fieldkof characteristic not 2 or l. If S is amaximal Weil-isotropic subgroup ofJH [l], thenJH /S is isomorphic to the Jacobian JX of some (possibly reducible) curve X . We investigate the Dolgachev– Lehavi method for constructing the curve X , simplifying their approach and making it more explicit. The result, at least for l = 3, is an efficient a...

Large interindividual differences exist in resting sympathetic nerve activity (SNA) among normotensive humans with similar arterial pressure (AP). We recently showed inverse relationships of resting SNA with cardiac output (CO) and vascular adrenergic responsiveness that appear to balance the influence of differences in SNA on blood pressure. In the present study, we tested whether nitric oxide...

We say that a countable discrete group Γ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every Γ- subalgebra M in L(Γ) is of form L(Λ) for some normal subgroup Λ◁Γ. show many “negatively curved” groups, including all torsion free non-amenable hyperbolic groups and with positive first L2-Betti number under mild assumption, certain finite direct product them have this p...

let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structur...

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

We introduce the problem of robust subgroup discovery, i.e., finding a set interpretable descriptions subsets that 1) stand out with respect to one or more target attributes, 2) are statistically robust, and 3) non-redundant. Many attempts have been made mine either locally subgroups tackle pattern explosion, but we first address both challenges at same time from global modelling perspective. F...