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

Mathematics

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

8 Scopus citations

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 (US)
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

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Mathematics(all)

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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",

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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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JF - Bulletin of the London Mathematical Society

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Word values in p-adic and adelic groups

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