  Let $\{ G_n\}_{n\in\w}$ be a closed tower of metrizable groups. Under a mild
condition called $(GC)$ and which is strictly weaker than $PTA$ condition
introduced in [22], we show that: (1) the inductive limit
$G=\mbox{g-}\underrightarrow{\lim}\, G_n$ of the tower is a Hausdorff group,
(2) every $G_n$ is a closed subgroup of $G$, (3) if $K$ is a compact subset of
$G$, then $K\subseteq G_m$ for some $m\in\omega$, (4) $G$ has a
$\mathfrak{G}$-base and countable tightness, (5) $G$ is an $\aleph$-space, (6)
$G$ is an Ascoli space if and only if either (i) there is $m\in\omega$ such
that $G_n$ is open in $G_{n+1}$ for every $n\geq m$, so $G$ is metrizable; or
(ii) all the groups $G_n$ are locally compact and $G$ is a sequential
non-Fr\'{e}chet--Urysohn space.
