Defining relations of classical orthogonal groups over commutative local rings (Q1902834)

Assume that \(\Lambda\) is an arbitrary commutative local ring with unit. We denote by \(O(n,\Lambda)\) the classical orthogonal group over the ring \(\Lambda\) of degree \(n\), i.e., the subgroup of matrices \(a\) of the complete linear group \(GL(n,\Lambda)\), for which \(aa'=e\) holds (\('\) is transposition, \(e\) is the unit matrix). The main objective is the description of the orthogonal group \(O(n,\Lambda)\), \(n\geq 2\), in terms of generators and relations over a commutative local ring \(\Lambda\) with the condition \((\Lambda^*)^2+\Lambda^2\subseteq(\Lambda^*)^2\).