2025/03/17 by Pradeep, Gayathry, Asokan, Ambily Ambattu, Kovilakam, Aparna Pradeep Vadakke
#11E70 #13C10 #19G99 #20H25 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.12839
We prove the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group, which was introduced by Amit Roy in 1968 and the Eichler-Siegel-Dickson transvection group, which is in literature in the works of Dickson, Siegel and Eichler, are equal over a commutative ring in which 2 is invertible. We prove the equality in the free case by considering the odd and even case separately and then generalize this result by using the local-global principle. This result generalizes previous results concerning the equality of elementary orthogonal transvection groups.