Shripad M. Garge

activity

20042025

most citedMaximal tori determining the algebraic group

9 citations · 10 across the 15 of their papers we have counts for

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13 papers · 1 filter

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 $E_{σ}^{'} (R, J)$ …

math.GR2024

A Frobenius-Type Formula for Compact Lie Groups

Shripad Garge, Uday Bhaskar Sharma

Let $G$ be a group and $α : G \times G \to G$ denote the commutator map. In the case of finite groups, Frobenius gave the formula to compute the cardinalities of the fibres $α^{-1}(…

math.GR2022

Twisted conjugacy in classical groups over certain domains of Characteristic $p > 0$

Shripad M. Garge, Oorna Mitra

Let $F$ be a subfield of the algebraic closure of a finite field $F_{p}$ , $p \neq = 2$ , and let $R$ denote any ring such that $F [t] \subset R ⊊ F (t)$ . Let $G$ be a cla…

math.GR2021

Asymptotics of commuting probabilities in reductive algebraic groups

Shripad M. Garge, Uday Bhaskar Sharma, Anupam Singh

Let $G$ be an algebraic group. For $d \geq 1$ , we define the commuting probabilities $c p_{d} (G) = \frac{d im ( C _{d} ( G ))}{d im ( G ^{d} )}$ , where $C_{d} (G)$ is the variety of c…

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

A Frobenius-Type Formula for Compact Lie Groups

Twisted conjugacy in classical groups over certain domains of Characteristic p>0

Asymptotics of commuting probabilities in reductive algebraic groups

Twisted conjugacy in classical groups over certain domains of Characteristic $p > 0$