Numbers of classes of classical groups

Abstract

In the paper, the description of the numbers and groups of classes of the simple classical indefinite groups over a fieldK of algebraic numbers in the canonical realizations is completed. A criterion for a simply connected semisimple algebraic group in some givenK-realization to be a one-class group is proved. A criterion for the existence of a one-class quadratic form among the forms ℚ–equivalent to a definite quadratic form inn>-3 variables over the field ℚ of rational numbers is obtained.