MathDBKourovka Notebook Problem 18.16
Kourovka Notebook Problem 18.16
For every -group and every normal subgroup , is again a -group? Equivalently, is the class of all -groups closed under taking normal subgroups?
Progress summary
A 2026 preprint settles one language version affirmatively but shows that a broader version fails, so the original problem is only partly resolved.
Kourovka Notebook Problem , attributed to Sh. S. Kemkhadze in 2014, asks whether the class of all -groups is closed under taking normal subgroups.
August 2026 development
Yuriy B. Glukhov reports an affirmative result for the parameter-allowed pure-language case, while the unrestricted expansion-language version fails. The result is presented as an answer to Problem , but the available abstract does not fully identify the correspondence with the original formulation.
Current status (as of August 2026): The parameter-allowed pure-language case is reported proved and the unrestricted expansion-language version disproved, while the exact status of the original formulation remains unclear.
Sources & referencesView supporting material
Primary source
Additional references
- A note on definable endomorphisms of ordered abelian groups — arXiv — Yuriy B. Glukhov
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