structure of the direct limit ${\mathrm g\mbox{-}\kern-2pt\varinjlim}G_n$ was discussed in [@Eda], [@HSTH], [@Glo03], [@Glo06], [@Glo08], [@TSH].

In this paper we shall show that under certain conditions on a tower of topological groups $(G_n)_{n\in{\omega}}$ the topology of the direct limit ${\mathrm g\mbox{-}\kern-2pt\varinjlim}G_n$ coincides with one (or all) of four simply described topologies $\LA[\tau]$, $\RA[\tau]$, $\LR[\tau]$ or $\RL[\tau]$ on the group $G=\bigcup_{n\in{\omega}}G_n$. These topologies are considered in Section \[s:top\]. In Sections \[s:PTA\] and \[s1:SIN\] we study two properties (${\mathrm{PTA}}$ and the balanced property) of a tower of topological groups $(G_n)_{n\in{\omega}}$ implying that the topology of ${\mathrm g\mbox{-}\kern-2pt\varinjlim}G_n$ coincides with the topology $\LR[\tau]$, which is the strongest among the four topologies on $G$. In Section \[s2:SIN\] we define another (bi-balanced) property of the tower $(G_n)$ guaranteeing that the topology of ${\mathrm g\mbox{-}\kern-2pt\varinjlim}G_n$ coincides with the topology $\RL[\tau]$, which is the weakest among the four topologies on $G$. In Section \[s:ulim-top\] we reveal the uniform nature of the topologies $\LA[\tau]$ and $\RA[\tau]$ and show that they coincide with the topologies of the uniform direct limits ${\mathrm u\mbox{-}\kern-2pt\varinjlim}G_n^{{\mathrm{L}}}$ and ${\mathrm u\mbox{-}\kern-2pt\varinjlim}G_n^R$ of the groups $G_n$ endowed with the left and right uniformities. In Section \[s:OP\] we sum up the results obtained in this paper and 