Abstract:
In the present paper we prove the reduction theorems for triple short root unipotent subgroups in Chevalley groups of type $\mathrm B_\ell$ and $\mathrm C_\ell$. The main result roughly speaking is the following. Any subgroup generated by a triple of subgroups in question (apart from one case) is conjugate to a subgroup of
$$
G(\mathrm B_4,K)U(\mathrm B_5,K)\quad\mathrm{or}\quad G(\mathrm C_4,K)U(\mathrm C_5,K),
$$
respectively.
Key words and phrases:Chevalley groups, root subgroups, unipotent radical.