Normalizer of twisted Chevalley groups over commutative rings

2025/03/21 by Shripad M. Garge, Deep H. Makadiya, Garge, Shripad M. +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Finite Group Theory Research

paper · pdf · doi:10.1016/j.jpaa.2025.108094

Abstract

Let R be a commutative ring with unity. Consider the twisted Chevalley group G_{π, σ} (Φ, R) of type ϕ over R and its elementary subgroup E'_{π, σ} (Φ, R). This paper investigates the normalizers of E'_{π, σ}(Φ, R) and G_{π, σ}(Φ, R) in the larger group G_{π, σ}(Φ, S), where S is an extension ring of R. We establish that under certain conditions on R these normalizers coincide. Moreover, in the case of adjoint type groups, we show that they are precisely equal to G_{π, σ}(Φ, R).

Citations

• On normal subgroups of twisted Chevalley groups over commutative rings

Cited by

• Automorphisms of Twisted Chevalley Groups of type ² D_ℓ (ℓ ≥ 4) over Local Rings

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