# Normal subgroups of Sylow subgroups in p-soluble groups

- Reference: `kourovka-21-64-normal-subgroups-of-sylow-subgroups-in-p-soluble-groups`
- Page: https://theoremdb.org/statements/kourovka-21-64-normal-subgroups-of-sylow-subgroups-in-p-soluble-groups
- Record maturity: Reviewed problem

## Problem

Is it true that if a normal subgroup A of a Sylow p-subgroup of a p-soluble finite group G has exponent pe, then the normal closure of A in G has (p, e)-bounded (or even e-bounded) p-length? This is Kourovka Notebook Problem \(21.64\).

## Status

The reviewed record remains open.

## Work

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `kourovka-21-64-normal-subgroups-of-sylow-subgroups-in-p-soluble-groups`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.