Improved K₁-stability for the embedding D₅ into E₆

Abstract

This article is dedicated to the surjective stability of the K₁-functor for Chevalley groups for the embedding D₅ into E₆. This case was already studied by Plotkin. In this article, we improve his result by showing that surjective stability holds under a weaker assumption on a ring. Another result of this article shows how the K₁-stability can help to study overgroups of subsystem subgroups.

Keywords:

• Chevalley groups
• K1-functor
• surjective stability

2010 Mathematics Subject Classification:

• 19B14 (primary)
• 20G35
• and 20G41(secondary)

Acknowledgment

I am very grateful to my advisor Nikolai Vavilov for the careful reading of this article and making important remarks and corrections.