Word values in p-adic and adelic groups

Nir Avni; Tsachik Gelander; Martin Kassabov; Aner Shalev

doi:10.1112/blms/bdt063

Word values in p-adic and adelic groups

Nir Avni, Tsachik Gelander, Martin Kassabov, Aner Shalev

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

Word values and word width in finite simple groups were studied extensively in recent years. In this paper, we study similar problems for simple algebraic groups over the p-adic integers, and sometimes over general local rings. In particular, under some conditions, we establish width 3 results for arbitrary words, as well as partial analogs of Ore conjecture on commutators.

Original language	English
Pages (from-to)	1323-1330
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	45
Issue number	6
DOIs	https://doi.org/10.1112/blms/bdt063
State	Published - Dec 2013

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/blms/bdt063

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title = "Word values in p-adic and adelic groups",

abstract = "Word values and word width in finite simple groups were studied extensively in recent years. In this paper, we study similar problems for simple algebraic groups over the p-adic integers, and sometimes over general local rings. In particular, under some conditions, we establish width 3 results for arbitrary words, as well as partial analogs of Ore conjecture on commutators.",

author = "Nir Avni and Tsachik Gelander and Martin Kassabov and Aner Shalev",

note = "Funding Information: Nir Avni was supported by NSF Grant DMS-0901638, Tsachik Gelander was supported by ERC grant 203418 and ISF grant 1003/11, Martin Kassabov was supported by NSF grant DMS-0900932 and Aner Shalev was supported by advanced ERC grant 247034 and BSF grant 2008194.",

year = "2013",

month = dec,

doi = "10.1112/blms/bdt063",

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pages = "1323--1330",

journal = "Bulletin of the London Mathematical Society",

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AU - Avni, Nir

AU - Gelander, Tsachik

AU - Kassabov, Martin

AU - Shalev, Aner

N1 - Funding Information: Nir Avni was supported by NSF Grant DMS-0901638, Tsachik Gelander was supported by ERC grant 203418 and ISF grant 1003/11, Martin Kassabov was supported by NSF grant DMS-0900932 and Aner Shalev was supported by advanced ERC grant 247034 and BSF grant 2008194.

PY - 2013/12

Y1 - 2013/12

N2 - Word values and word width in finite simple groups were studied extensively in recent years. In this paper, we study similar problems for simple algebraic groups over the p-adic integers, and sometimes over general local rings. In particular, under some conditions, we establish width 3 results for arbitrary words, as well as partial analogs of Ore conjecture on commutators.

AB - Word values and word width in finite simple groups were studied extensively in recent years. In this paper, we study similar problems for simple algebraic groups over the p-adic integers, and sometimes over general local rings. In particular, under some conditions, we establish width 3 results for arbitrary words, as well as partial analogs of Ore conjecture on commutators.

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U2 - 10.1112/blms/bdt063

DO - 10.1112/blms/bdt063

M3 - مقالة

SN - 0024-6093

VL - 45

SP - 1323

EP - 1330

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 6

ER -

Word values in p-adic and adelic groups

Abstract

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