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In this paper we show that stable rank of the C -algebras of simply connected, amenable Lie groups of type I is estimated by complex dimension of the spaces of all characters of these groups. It is extended to the connected case, by which we show that product formula of stable rank holds for the group C -algebras of connected, amenable Lie groups of type I. For further estimation of stable rank of those group C -algebras, we need the conditions of the radicals of those groups.

Stable rank of the $C^*$-algebras of amenable Lie groups of type I