Activities This Week

Speaker: Yves de Cornulier (CNRS, University Lyon 1)

Place: Room -101, Math building (58)

Title: near actions

Abstract A near permutation of a set $X$ is a permutations “up to finite subset”. It can be formally defined as the germ at infinity of a homeomorphism of the one-point compactification of $X$. A near action of a group is a homomorphism into the group of near permutations of a set. We notably study realizability of near actions, namely understanding obstructions to being induced by a genuine action. These concepts can be applied to the study of the class $(M)$ of maximal abelian subgroups of $S_\omega/fin$, where $S_\omega$ is the group of permutations of the countable set $\omega$ and $fin$ is its normal subgroup of finitely supported permutations. Uncountable groups in the class $(M)$ have been studied by Shelah and Steprans (2007). We characterize countable abelian groups that occur in the class $(M)$.