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arXiv · 1912.09325

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

Pavel Gvozdevsky
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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.

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Pavel Gvozdevsky. 2019-12-19. Improved $K_1$-stability for the embedding $D_5$ into $E_6$. https://doi.org/10.1080/00927872.2020.1775239

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