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On root-involutions and root-subgroups of \(E_6(K)\) for fields \(K\) of characteristic two. (English) Zbl 1467.17006

Summary: The purpose of this paper is to investigate the root-involutions and root-subgroups of the Chevalley group \(E_6(K)\) for fields \(K\) of characteristic two. The approach we follow is elementary and self-contained depends on the notion of \(M\)-sets which we have introduced in [the authors, Beitr. Algebra Geom. 58, No. 3, 529–534 (2017; Zbl 1378.17023)]. The approach is elementary on the account that it consists of little more than naive linear algebra. It is remarkable to mention that Chevalley groups over fields of characteristic two have not much been researched. This work may contribute in this regard. This paper is divided into three main sections: the first section is a combinatorial section, the second section is on relations among \(M\)-sets, the last one is on Lie algebra.

MSC:

17B25 Exceptional (super)algebras
17B45 Lie algebras of linear algebraic groups
20G15 Linear algebraic groups over arbitrary fields

Citations:

Zbl 1378.17023
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References:

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