Pith. sign in

REVIEW 1 cited by

Automorphism invariance and identities

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0812.1359 v2 pith:YMP2SFX5 submitted 2008-12-07 math.GR math.RA

Evgenii I. Khukhro , Anton A. Klyachko , Natalia Yu. Makarenko , Yulia B. Melnikova This is my paper · ORCID
classification math.GRmath.RA
keywords largeholdsidentitiessolvablesubgroupvirtuallyalgebrasapplication
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the word "large", we obtain many interesting facts. These results cannot be extended to arbitrary (non-multilinear) identities. As an application, we give a sharp estimate for the `virtual derived length' of (virtually solvable)-by-(virtually solvable) groups.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Invariant systems of representatives, or The cost of symmetry

    math.CO 2019-08 conditional novelty 6.0 of 10

    Under any group action, a finite system of representatives of size r for a bounded family of sets can be replaced by an invariant system of representatives of size at most r times the maximum set size.

Pith tools