Unitary Groups Under The Λ-stable Range Condition

In this thesis, we use the concept of Λ-stable range condition introduced by A. Bak and Guoping Tang in [1] to research the unitary groups (without hyperbolic basis) with some Witt index conditions. In this thesis, we first give a brief introduction to classical groups. When form ring satisfies certain Λ-stable range condition, we use the results in [2]to prove the normality of a unitary congruence subgroup EU(M,I,T) andan important commutator equation of unitary congruence subgroups. Then, we prove the existence of an elementary Eichler transformation in asubgroup which is normalized by elementary subgroup EU(M). Finally, we discuss the problem sandwich classifications of unitary groups.