The notion of an algebra that is locally embeddable into finite
dimensional algebras (LEF) and
the
notion of an LEF group was introduced by Gordon and Vershik in
[GoVe]. M. Ziman proved in [Zi] that the group algebra of a
group $G$ is an LEF algebra if and only if $G$ is an
LEF
group. He conjectured that an algebra generated as a vector space
by a multiplicative subgroup
$G$
of its invertible elements is an LEF algebra if and only if $G$ is an
LEF group. In this paper we give a characterization
of
the invertible elements of an LEF algebra and use it to construct a
counterexample to this
conjecture.