Improved $K_1$-stability for the embedding $D_5$ into $E_6$

Pavel Gvozdevsky

doi:10.1080/00927872.2020.1775239

paper

Improved $K_{1}$ -stability for the embedding $D_{5}$ into $E_{6}$

arXiv:1912.09325 · doi:10.1080/00927872.2020.1775239

Abstract

This paper is dedicated to the surjective stability of the $K_{1}$ -functor for Chevalley groups for the embedding $D_{5}$ into $E_{6}$ . This case was already studed by Plotkin. In the present paper, we improve his result by showing that surjective stability holds under a weaker assumption on a ring. Another result of the present paper shows how the $K_{1}$ -stability can help to study overgroups of subsystem subgroups.

11 pages, 4 figures, submitted to "Communications in algebra"

Improved K1​-stability for the embedding D5​ into E6​

Abstract

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Improved $K_{1}$ -stability for the embedding $D_{5}$ into $E_{6}$