Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4660885 | Topology and its Applications | 2008 | 13 Pages |
Abstract
Fujiwara [K. Fujiwara, The second bounded cohomology of a group with infinitely many ends, math.GR/9505208] conjectured that the second bounded cohomology of a group is zero or infinite-dimensional as a vector space over R. However, it is known that there are some linear groups for which the second bounded cohomology is not zero but finite-dimensional. In this paper, by using the transfinitely extended derived series, we prove that Fujiwara's conjecture is true for the hypo-Abelian groups, that is, groups with no non-trivial perfect subgroups.
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