In 2005, V.A. Petrov introduced a new type of classical-like group known as the odd unitary group, which generalises all the classical Chevalley groups, the unitary groups U2n+1(R) of E. Abe, and the classical-like groups such as Bak’s hyperbolic unitary groups and G. Tang’s Hermitian groups. The importance of this group is that it includes the odd dimensional orthogonal group O2n+1, as well as the unitary groups U2n+1(R) of Abe, which was not covered in the theory of quadratic or Hermitian groups. In this talk, I will discuss the definition of Petrov’s odd unitary group and an important subgroup of it called the odd elementary hyperbolic unitary group.
