Publication

On growth and torsion of groups

2009
Journal Articles

Abstract

We give a subexponential upper bound and a superpolynomial lower bound on the growth function of the Fabrykowski-Gupta group.

Official source

https://infoscience.epfl.ch/entities/publication/1f3a7640-f549-43ad-8225-a74699981d15

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2009
Journal Articles

Abstract

We give a subexponential upper bound and a superpolynomial lower bound on the growth function of the Fabrykowski-Gupta group.

Official source

https://infoscience.epfl.ch/entities/publication/1f3a7640-f549-43ad-8225-a74699981d15

About this result

Related concepts (13)

L-notation

L-notation is an asymptotic notation analogous to big-O notation, denoted as for a bound variable tending to infinity. Like big-O notation, it is usually used to roughly convey the rate of growth of a function, such as the computational complexity of a particular algorithm. It is defined as where c is a positive constant, and is a constant . L-notation is used mostly in computational number theory, to express the complexity of algorithms for difficult number theory problems, e.g.

Big O notation

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows.

Algebraic group

In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example, orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties.

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