Deep H. Makadiya

collaborators

10 papers

math.GR2026

Automorphisms of Twisted Chevalley Groups over Commutative Rings

Elena I. Bunina, Deep H. Makadiya

We classify all abstract automorphisms of the elementary and full twisted Chevalley groups of types $^{2} A_{ℓ}$ ( $ℓ \geq 3$ ), $^{2} D_{ℓ}$ ( $ℓ \geq 4$ ), $^{2} E_{6}$ , and $^{3} D_{4}$ …

math.GR2026

Automorphisms of triality groups over local rings

Elena Bunina, Avi Berezovskiy, Deep Makadiya

Let $R$ be a nonzero commutative local ring with $2, 3 \in R^{\times}$ , and let $ρ\in\Aut(R)$ satisfy $ρ^3=\id$. We classify abstract automorphisms of the elementary and full triality…

math.GR2026

Automorphisms of twisted Chevalley groups of type $^{2} E_{6}$ over local rings

Elena I. Bunina, Deep H. Makadiya

We classify abstract automorphisms of the elementary and full twisted Chevalley groups of type $^{2} E_{6}$ over commutative local rings with involution and $2$ invertible, for both i…

math.GR2026

Automorphisms of Twisted Chevalley Groups of type $^{2} A_{3}$ and $^{2} A_{4}$ over Local Rings

Elena I. Bunina, Deep H. Makadiya

We give a complete classification of the automorphisms of twisted Chevalley groups of types $^{2} A_{3}$ and $^{2} A_{4}$ , and of their elementary subgroups, over commutative local rings…

math.GR2026

Automorphisms of Twisted Chevalley Groups of type $^{2} D_{ℓ} (ℓ \geq 4)$ over Local Rings

Elena I. Bunina, Deep H. Makadiya

We prove that all automorphisms of twisted Chevalley groups of type $^{2} D_{ℓ}$ , $ℓ \geq 4$ , and their elementary subgroups over commutative local rings with $1/2$ are standard. M…

math.GR2026

Automorphisms of Twisted Chevalley Groups of type $^{2} A_{ℓ} (ℓ \geq 5)$ over Local Rings

Elena I. Bunina, Deep H. Makadiya

This paper is the first in a series devoted to the classification of automorphisms and isomorphisms of twisted Chevalley groups over commutative rings. In the present paper, we pro…

math.GR2025

Some Properties of Twisted Chevalley Groups

Deep H. Makadiya

This thesis investigates certain structural properties of twisted Chevalley groups over commutative rings, focusing on three key problems. Let $R$ be a commutative ring satisfying…

math.GR2025

Triangular and Unitriangular Factorization of Twisted Chevalley Groups

Shripad M. Garge, Deep H. Makadiya

The existence of triangular and unitriangular factorizations has been extensively studied for untwisted Chevalley groups, as well as for twisted Chevalley groups of types other tha…

math.GR2025

Normalizer of Twisted Chevalley Groups over Commutative Rings

Shripad M. Garge, Deep H. Makadiya

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 inv…

math.GR2025

On Normal Subgroups of Twisted Chevalley Groups over Commutative Rings

Shripad M. Garge, Deep H. Makadiya

In this paper, we prove two structure theorems for twisted Chevalley groups $G_{σ} (R)$ over a commutative ring $R$ with unity. The first theorem concerns the normality of $E_{σ}^{'} (R, J)$ …

Automorphisms of Twisted Chevalley Groups over Commutative Rings

Automorphisms of triality groups over local rings

Automorphisms of twisted Chevalley groups of type 2E6​ over local rings

Automorphisms of Twisted Chevalley Groups of type 2A3​ and 2A4​ over Local Rings

Automorphisms of Twisted Chevalley Groups of type 2Dℓ​ (ℓ≥4) over Local Rings

Automorphisms of Twisted Chevalley Groups of type 2Aℓ​ (ℓ≥5) over Local Rings

Some Properties of Twisted Chevalley Groups

Triangular and Unitriangular Factorization of Twisted Chevalley Groups

Normalizer of Twisted Chevalley Groups over Commutative Rings

On Normal Subgroups of Twisted Chevalley Groups over Commutative Rings

Automorphisms of twisted Chevalley groups of type $^{2} E_{6}$ over local rings

Automorphisms of Twisted Chevalley Groups of type $^{2} A_{3}$ and $^{2} A_{4}$ over Local Rings

Automorphisms of Twisted Chevalley Groups of type $^{2} D_{ℓ} (ℓ \geq 4)$ over Local Rings

Automorphisms of Twisted Chevalley Groups of type $^{2} A_{ℓ} (ℓ \geq 5)$ over Local Rings