Normality theorem for elementary symplectic group with respect to an alternating form
Group Theory
2022-11-04 v1 Commutative Algebra
Abstract
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.
Cite
@article{arxiv.2211.01416,
title = {Normality theorem for elementary symplectic group with respect to an alternating form},
author = {Ruddarraju Amrutha and Pratyusha Chattopadhyay},
journal= {arXiv preprint arXiv:2211.01416},
year = {2022}
}