scholarly journals Rigid abelian groups and the probabilistic method

2012 ◽  
pp. 17-30
Author(s):  
Gábor Braun ◽  
Sebastian Pokutta
Keyword(s):  
Abelian Groups ◽  
Probabilistic Method

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

DEFINITION OF TIME SPENT ON REPAIR OF BUS TRANSMISSION UNITS TAKING INTO ACCOUNT TECHNOLOGICAL EQUIPMENT RELIABILITY

2020 ◽  
Vol 2020 (9) ◽  
pp. 29-33
Author(s):  
Sergey Bulatov
Keyword(s):  
Negative Impact ◽  
Probabilistic Method ◽  
Technological Equipment ◽  
Quality And Safety ◽  
Transmission Unit ◽  
Equipment Reliability ◽  
Hours Of Work ◽  
Definition Of ◽  
Time Decrease

The paper purpose is the effectiveness estimation in the technological equipment use, taking into account its reliability and productivity for defective transmission units of buses. The problem consists in the determination of time to be spent on repair of bus transmission units taking into account technological equipment reliability. In the paper there is used a probabilistic method for the prediction bus transmission units, and also a method of the dynamics of averages which allow ensuring minimum of costs for units downtime during repair and equipment cost. The need for repair of transmission units (gear box) arises on an average after 650 hours, the average productivity of the bench makes 4.2 bus / hour. The bench fails on the average after 4600 hours of work, the average time of the bench makes 2 hours. In such a way the solution of the problem specified allows analyzing the necessity of time decrease for transmission unit repair to avoid long downtimes of buses in repair areas without negative impact upon high repair quality and safety during the further operation.

scholarly journals Embedding the Picard group inside the class group: the case of $$\mathbb {Q}$$-factorial complete toric varieties

2021 ◽  
Author(s):  
Michele Rossi ◽  
Lea Terracini
Keyword(s):  
Free Group ◽  
Toric Variety ◽  
Class Group ◽  
Abelian Groups ◽  
Toric Varieties ◽  
Picard Group ◽  
Closed Field ◽  
Finitely Generated ◽  
Free Part ◽  
Canonical Injection

AbstractLet X be a $$\mathbb {Q}$$ Q -factorial complete toric variety over an algebraic closed field of characteristic 0. There is a canonical injection of the Picard group $$\mathrm{Pic}(X)$$ Pic ( X ) in the group $$\mathrm{Cl}(X)$$ Cl ( X ) of classes of Weil divisors. These two groups are finitely generated abelian groups; while the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of $$\mathrm{Pic}(X)$$ Pic ( X ) in $$\mathrm{Cl}(X)$$ Cl ( X ) is contained in a free part of the latter group.

Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

2021 ◽  
pp. 1-36
Author(s):  
ARIE LEVIT ◽  
ALEXANDER LUBOTZKY
Keyword(s):  
Ergodic Theorem ◽  
Abelian Groups ◽  
Wreath Products ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Amenable Groups ◽  
Pointwise Ergodic Theorem ◽  
Lamplighter Group ◽  
Invariant Random Subgroups

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

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