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The Theory of Infinite Soluble Groups

John C. Lennox and Derek J. S. Robinson

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198507284
eISBN:
9780191709326
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507284.001.0001
Subject:
Mathematics, Pure Mathematics

This book provides a comprehensive account of the theory of infinite soluble groups, from its foundations up to research level. Topics covered include: polycyclic groups, Cernikov groups, Mal’cev ... More


NILPOTENT GROUPS

John C. Lennox and Derek J. S. Robinson

in The Theory of Infinite Soluble Groups

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198507284
eISBN:
9780191709326
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507284.003.0002
Subject:
Mathematics, Pure Mathematics

This chapter discusses extraction of roots in nilpotent groups. Topics covered include the Mal’cev completion for a torsion-free nilpotent group, the commutator collection process, and isolators.


Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms

Alexandru D. Ionescu, Akos Magyar, and Stephen Wainger

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0007
Subject:
Mathematics, Numerical Analysis

This chapter concentrates on the averages of functions along polynomial sequences in discrete nilpotent groups, illustrating the problems that arise from studying these averages. Though special ... More


ROUGH PATHS

Terry Lyons and Zhongmin Qian

in System Control and Rough Paths

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198506485
eISBN:
9780191709395
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506485.003.0003
Subject:
Mathematics, Probability / Statistics

This chapter defines rough paths. If the path has good smoothness properties, then its chords (the Abelian version of the description) provide an adequate description and can be used to predict its ... More


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