Growth and generation in SL_2(Z/pZ)

HA Helfgott

Growth and generation in SL_2(Z/pZ)

HA Helfgott

School of Mathematics

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Abstract

We show that every subset of SL_2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL_2(Z/pZ), every element of SL_2(Z/pZ) can be expressed as a product of at most O((log p)^c) elements of the union of A and A^{-1}, where c and the implied constant are absolute.

Translated title of the contribution	Growth and generation in SL_2(Z/pZ)
Original language	English
Publisher	Cornell University Press
Publication status	Published - 11 Jun 2007

Bibliographical note

Other: To appear in Annals of Mathematics

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http://www.arxiv.org/abs/math.GR/0509024

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title = "Growth and generation in SL\_2(Z/pZ)",

abstract = "We show that every subset of SL\_2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL\_2(Z/pZ), every element of SL\_2(Z/pZ) can be expressed as a product of at most O((log p)\textasciicircum{}c) elements of the union of A and A\textasciicircum{}\{-1\}, where c and the implied constant are absolute.",

author = "HA Helfgott",

note = "Other: To appear in Annals of Mathematics",

year = "2007",

month = jun,

day = "11",

language = "English",

publisher = "Cornell University Press",

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T1 - Growth and generation in SL_2(Z/pZ)

AU - Helfgott, HA

N1 - Other: To appear in Annals of Mathematics

PY - 2007/6/11

Y1 - 2007/6/11

N2 - We show that every subset of SL_2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL_2(Z/pZ), every element of SL_2(Z/pZ) can be expressed as a product of at most O((log p)^c) elements of the union of A and A^{-1}, where c and the implied constant are absolute.

AB - We show that every subset of SL_2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL_2(Z/pZ), every element of SL_2(Z/pZ) can be expressed as a product of at most O((log p)^c) elements of the union of A and A^{-1}, where c and the implied constant are absolute.

M3 - Web publication/site

PB - Cornell University Press

ER -

Growth and generation in SL_2(Z/pZ)

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