Shripad M. Garge

collaborators

4 papers

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 $G_{I ¨} (R)$ over a commutative ring $R$ with unity. The first theorem concerns the normality of $E'_Ï(R,J…

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 $G_{I ¨ , I ¨ } (I^¦, R)$ of type $I ¨ $ over $R$ and its elementary subgroup $E_{I ¨ , I ¨ }^{'} (I^¦, R)$ . This pa…

math.GR2024

A Frobenius-Type Formula for Compact Lie Groups

Shripad Garge, Uday Bhaskar Sharma

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