Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group

Nguyen Ngoc Hung; Yong Yang

Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group

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 1905.10512 v1 pith:PQXRLFJ5 submitted 2019-05-25 math.GR math.RT

Nguyen Ngoc Hung , Yong Yang This is my paper · ORCID

classification math.GRmath.RT

keywords abeliancharacterdegreefinitegrouplargestnilpotentsubgroups

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

Let $H$ be an abelian subgroup of a finite group $G$ and $\pi$ the set of prime divisors of $|H|$. We prove that $|H O_{\pi}(G)/ O_{\pi}(G)|$ is bounded above by the largest character degree of $G$. A similar result is obtained when $H$ is nilpotent.

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

Learned LSM-trees: Two Approaches Using Learned Bloom Filters
cs.DS 2025-07 reject novelty 4.0 of 10

A classifier that skips Bloom filter probes can halve measured GET latency in an LSM-tree but introduces false negatives, while a learned Bloom filter cuts per-level memory 70-80% with zero false negatives in static tests.

Pith tools