Pith. sign in

REVIEW 2 cited by

Characters of diagonal products and Hilbert-Schmidt stability

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 2407.11608 v2 pith:4C4S2MIW submitted 2024-07-16 math.GR

Alon Dogon , Arie Levit , Itamar Vigdorovich This is my paper
classification math.GR
keywords stabilitygroupshilbert-schmidtcharactersdiagonalfamilygrowthproducts
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We initiate a quantitative study of Hilbert-Schmidt stability for infinitely presented groups through the novel notion of stability radius growth. We exhibit an uncountable family of Hilbert-Schmidt stable amenable groups with arbitrarily large such growth. In particular, this answers a question of Lubotzky. Our approach is based on the character-theoretic stability criterion of Hadwin and Shulman. We classify the characters of alternating and elementary enrichments as well as diagonal products, including the classical family of B.H. Neumann groups.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Polynomial Hilbert-Schmidt stability of the lamplighter group

    math.GR 2026-07 conditional novelty 8.0 of 10 full

    The lamplighter group has stability radius growth ⪯ r^21 and stability rate ≥ cκ^70, giving the first explicit polynomial Hilbert–Schmidt stability bounds for an infinitely presented group.

  2. Groups with arbitrarily poor permutation stability

    math.GR 2026-04 unverdicted novelty 7.0 of 10

    Finitely generated groups exist that are permutation stable but exhibit arbitrarily bad quantitative stability, making sample-and-substitute algorithms very slow at checking relations.

Pith tools