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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



A new measure of growth for groups and algebras

Author: Waldemar Hołubowski
Translated by: N. A. Vavilov
Original publication: Algebra i Analiz, tom 19 (2007), nomer 4.
Journal: St. Petersburg Math. J. 19 (2008), 545-560
MSC (2000): Primary 15A30, 16P90, 20E07; Secondary 06D99, 16S50, 17B60, 20E15
Published electronically: May 9, 2008
MathSciNet review: 2381933
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Abstract | References | Similar Articles | Additional Information


The notion of a bandwidth growth is introduced, which generalizes the growth of groups and the bandwidth dimension, first discussed by J. Hannah and K. C. O’Meara for countable-dimensional algebras. The new measure of growth is based on certain infinite matrix representations and on the notion of growth of nondecreasing functions on the set of natural numbers. Two natural operations are defined on the set $\Omega ^{\star }$ of growths. With respect to these operations, $\Omega ^{\star }$ forms a lattice with many interesting algebraic properties; for example, $\Omega ^{\star }$ is distributive and dense and has uncountable antichains.

This new notion of growth is applied in order to define bandwidth growth for subgroups and subalgebras of infinite matrices and to study its properties.

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Additional Information

Waldemar Hołubowski
Affiliation: Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Keywords: Growth of groups, growth of algebras, bandwidth growth, string
Received by editor(s): August 15, 2006
Published electronically: May 9, 2008
Article copyright: © Copyright 2008 American Mathematical Society