Strong nuclearity of dual groups

Strongly nuclear spaces were introduced by Martineau and Brudovskij in the sixties. It is known that the dual space of a metrizable nuclear space is not only nuclear, but even strongly nuclear. Nuclear groups were introduced in [4]. They form a class of abelian topological groups which is an analogue of the class of nuclear spaces. It was proved in [4] that the dual group of a metrizable nuclear group is a nuclear group again. In this paper we introduce strongly nuclear groups, an analogue of strongly nuclear spaces, and prove that the dual group of a metrizable nuclear group is strongly nuclear.