Properties of final unrefinable chains of groups topologies

V. I. Arnautov

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2010), pp. 3-19.

Résumé

Let $G$ be a nilpotent group and $(\mathfrak{M},)$ be the lattice of all group topologies or the lattice of all group topologies in each of which the group $G$ possesses a basis of neighborhood of unit consisting of subgroups. If $\tau$ and ${\tau }^{\prime }$ are group topologies from $\mathfrak{M}$ such that $\tau ={\tau }_0{\prec }_{\mathfrak{M}}{\tau }_1{\prec }_{\mathfrak{M}}\dots {\prec }_{\mathfrak{M}}{\tau }_n={\tau }^{\prime }$, then $k\le n$ for any chain $\tau ={\tau }_0^{\prime }{\tau }_1^{\prime }\dots {\tau }_k^{\prime }={\tau }^{\prime }$ of topologies from $\mathfrak{M}$.

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