We classify the finite connected-homogeneous digraphs, as well as the infinite locally finite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

Local sentences and the formal languages they define were introduced by Ressayre in [Res88]. We prove that locally finite ω-languages and effective analytic sets have the same topological complexity: the Borel and Wadge hierarchies of the class of locally finite ω-languages are equal to the Borel and Wadge hierarchies of the class of effective analytic sets. In particular, for each non-null rec...

the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

These notes are defining the notion of centric linking system for a locally finite group. If group G has countable Sylow p-subgroups, we prove that, with finiteness condition on set intersections p-completion its classifying space is homotopy equivalent to nerve system.