Minimal length factorizations of finite simple groups of Lie type by
unipotent Sylow subgroups

Martino Garonzi; Dan Levy; Attila Maróti; Iulian I. Simion

doi:10.1515/jgth-2015-0051

Published by De Gruyter January 8, 2016

Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups

Martino Garonzi , Dan Levy , Attila Maróti and Iulian I. Simion

From the journal Journal of Group Theory

https://doi.org/10.1515/jgth-2015-0051

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Abstract

We prove that every finite simple group G of Lie type satisfies G = UU^-UU^-, where U is a unipotent Sylow subgroup of G and U^- is its opposite. We also characterize the cases for which G = UU^-U. These results are best possible in terms of the number of conjugates of U in the above factorizations.

Funding source: MIUR

Award Identifier / Grant number: PRIN Group theory and applications

Funding source: Alexander von Humboldt Fellowship for Experienced Researchers

Funding source: MTA

Award Identifier / Grant number: Rényi "left Lendület” Groups and Graphs Research Group

Funding source: OTKA

Award Identifier / Grant number: K84233

Funding source: University of Padova

Award Identifier / Grant number: CPDR131579/13

Funding source: University of Padova

Award Identifier / Grant number: CPDA125818/12

Received: 2015-8-27

Published Online: 2016-1-8

Published in Print: 2016-3-1

Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups

Abstract

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