# Finite extensions in Kropholler’s hierarchy

- Reference: `kourovka-21-36-finite-extensions-in-kropholler-s-hierarchy`
- Page: https://theoremdb.org/statements/kourovka-21-36-finite-extensions-in-kropholler-s-hierarchy
- Record maturity: Reviewed problem

## Problem

Kropholler’s hierarchy (see 15.45) is closed under finite extensions, that is, (Hα F)F ⊆ Hα F for every α (P. Kropholler, J. Pure Appl. Algebra, 90 (1993), 55-67). Let a hierarchy of tdlc groups HK be defined analogously to Kropholler’s hierarchy in 15.45, with K being the class of profinite groups and with the cell stabilisers of the admissible action required to be open. Is it true that HK is closed under profinite extensions, that is, (Hα K)K ⊆ Hα K for every α? This is Kourovka Notebook Problem \(21.36\).

## Status

The reviewed record remains open.

## Work

### Working on this

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## References

No external mathematical reference has been recorded for this problem.