Discussion Of The General Hermitian Group And Its Subgroup

The K -theory of forms is a research branch of the K -theory. The hermitian forms plays an important role in the K -theory of forms, While it is necessary to discuss the general hermitian groups and its elementary subgroups for studying the AT, -functor and K2 -functor of the hermitian forms. In this thesis, The author first tells explicitly that the origin, research object, function in mathematics of the K -theory and the developing history and the present research conditions of the K-theory of forms , Then simplifies the relations satisfied by the generators of the elementary group EQ2n(R,∧)of unitary group GQ2n(R,∧\), And then in the form of transvection plays emphasis on discussing the generators of the elementary group EH2n(R,a1,...,ar) of the general hermitian group GH2n(R,a1,...,ar) and their satisfying relations. Finally using the ∧-stable range condition which was introduced by Bak and Guo Ping Tang in their paper Stability for Hermitian K1, The author proves that the normality of elementary subgroup of hermitian group and the stability of hermitian AT,-group.