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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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