Another presentation of orthogonal Steinberg groups
Egor Voronetsky

TL;DR
This paper demonstrates a new presentation of orthogonal Steinberg groups using the pro-group approach and constructs analogs of ESD-transvections under certain conditions.
Contribution
It introduces a novel presentation for orthogonal Steinberg groups and constructs ESD-transvections analogs within the pro-group framework.
Findings
Established van der Kallen's presentation for orthogonal Steinberg groups.
Constructed ESD-transvections analogs in orthogonal Steinberg pro-groups.
Extended the understanding of the structure of orthogonal Steinberg groups.
Abstract
We use the pro-group approach to show that admits van der Kallen's "another presentation", where is a module over a commutative ring with sufficiently isotropic quadratic form . Moreover, we construct an analog of ESD-transvections in orthogonal Steinberg pro-groups under some assumptions on their parameters.
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