arXiv subjects

Ruddarraju Amrutha

Publications and source records attributed to Ruddarraju Amrutha.

4 recordsLinked to original sources

arXiv2026

Normality of Relative Elementary Tranvection Groups

A. A. Suslin and V. I. Kopeiko proved that the elementary linear, symplectic, and orthogonal groups are normal in the general linear group, symplectic group, and orthogonal group respectively. They also proved relative versions of these normality results with respect to an ideal of a ring. A. Bak, R. Basu, and R. A. Rao proved that the linear, symplectic, and orthogonal transvection groups are normal in the respective automorphism groups. These results are generalizations of the normality results by Suslin and Kopeiko in the setup of modules. In this paper, we prove stronger versions of the normality results proved by Bak, Basu, and Rao, which say that the relative transvection groups are normal in the respective automorphism groups.

math.GR↗

arXiv2025

Normality of Vaserstein group

A.A. Suslin proved a normality theorem for an elementary linear group and V.I. Kopeiko extended this result of Suslin for a symplectic group defined with respect to the standard skew-symmetric matrix of even size. We generalized the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one. Vaserstein group is an extension of a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one in the set up of projective modules. Here we prove a normality theorem for Vaserstein group.

math.AC↗

arXiv2024

Equality of elementary symplectic group and symplectic group

V.I. Kopeiko proved that over a euclidean ring, the symplectic group defined with respect to the standard skew-symmetric matrix is same as the elementary symplectic group. Here we generalise the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one.

math.AC↗

arXiv2022

Normality theorem for elementary symplectic group with respect to an alternating form

A.A. Suslin proved a normality theorem for an elementary linear group, which says that an elementary linear group of size bigger than or equal to 3 over a commutative ring with unity is normal in the general linear group of same size. Subsequently, V.I. Kopeiko extended this result of Suslin for a symplectic group defined with respect to the standard skew-symmetric matrix of even size. Here we generalise the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of even size of Pfaffian one.

math.GR↗