2025/02/07 by Shripad M. Garge, Deep H. Makadiya, Garge, Shripad M. +1 · 3 citations
Mathematics · #Finite Group Theory Research #Advanced Topics in Algebra #Advanced Algebra and Geometry
paper · pdf · doi:10.1016/j.jalgebra.2025.09.028
In this paper, we prove two structure theorems for twisted Chevalley groups Gσ(R) over a commutative ring R with unity. The first theorem concerns the normality of E'σ(R,J), the elementary congruence subgroups at level J, in the group Gσ(R). The second theorem classifies all subgroups of Gσ(R) normalized by its elementary subgroup E'σ(R). Along the way, we obtain several interesting results. For instance, when R is a semilocal ring, we show that Gσ(R) can be expressed as the (internal) product of E'σ(R) and the maximal torus Tσ(R) of Gσ(R).