Groups possessing extensive hierarchical decompositions

Details Groups possessing extensive hierarchical decompositions Groups possessing extensive hierarchical decompositions

2009-08-25

arxiv.org/abs/0908.3669v1

Mathematics

Group Theory

9 pages

Scientific paper

Kropholler's class of groups is the smallest class of groups which contains all finite groups and is closed under the following operator: whenever $G$ admits a finite-dimensional contractible $G$-CW-complex in which all stabilizer groups are in the class, then $G$ is itself in the class. Kropholler's class admits a hierarchical structure, i.e., a natural filtration indexed by the ordinals. For example, stage 0 of the hierarchy is the class of all finite groups, and stage 1 contains all groups of finite virtual cohomological dimension. We show that for each countable ordinal $\alpha$, there is a countable group that is in Kropholler's class which does not appear until the $\alpha+1$st stage of the hierarchy. Previously this was known only for $\alpha= 0$, 1 and 2. The groups that we construct contain torsion. We also review the construction of a torsion-free group that lies in the third stage of the hierarchy.

Affiliated with

Also associated with

No associations

Rating

Groups possessing extensive hierarchical decompositions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Groups possessing extensive hierarchical decompositions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Groups possessing extensive hierarchical decompositions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233667