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Journal of Lie Theory 27 (2017), No. 4, 1107--1118
Copyright Heldermann Verlag 2017

On Construction of the Maximal Parabolic Subgroup P1 of E6(K) for Fields K of Characteristic Two

Abdullah Alazemi
Dept. of Mathematics, Faculty of Science, Kuwait University, Khalediya, Kuwait

Mashhour Bani-Ata
Dept. of Mathematics, Faculty of Science, PAAET, Ardiya, Kuwait

The notion of M-sets has been introduced by the second author to give an elementary construction for the Lie algebras of type E6 and F4 and the Chevalley groups E6(K), F4(K), and 2E6(K) over fields K of characteristic two. The aim of this article is to use the notion of M-sets to give an elementary and self-contained construction of the maximal parabolic subgroup P1 of E6(K) using Levi components and unipotent radical root subgroups of E6(K).

Keywords: Maximal parabolic, Levi component, unipotent radical, M-sets.

MSC: 17B25, 17B54, 20G20

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