Skip to content
DraconiticResearch
Search Sources API
186,631 studies31 sourcesUpdated 21 min ago
PreprintarXiv licencearXiv

Comparing word probabilities in finite groups

  • Lorenzo Putignano
  • Matteo Vannacci
Open at sourcePDFDOICite

Abstract

We use results from extremal graph theory and analysis to compare word probabilities in finite groups. In particular, we show that the probability of satisfying the 2-Engel word admits a positive lower bound in terms of the probability that an element has order dividing 3. More generally, using a group removal lemma, we obtain analogous bounds for xm-good words.

Related

  1. On the word and period growth of some groups of tree automorphisms
    Laurent Bartholdi, Zoran Sunik
    Communications in AlgebraPeer-reviewedLicence not statedFull text44 citedAlgebra & number theoryHAL
  2. Word Trace Formulas over Compact Groups and Connected Cumulants
    Liviu Paunescu, Florin Radulescu
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  3. The word problem in verbal products of groups
    Javier Brude, Román Sasyk
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Images of word maps with constants on algebraic groups
    Vadim Alekseev, Jakob Schneider
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv
  5. Word Length and Diameter in Permutation Groups
    Markus Lohrey, Alexander Thumm
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{putignano2026comparing,
  title = {{Comparing word probabilities in finite groups}},
  author = {Lorenzo Putignano and Matteo Vannacci},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23100},
  eprint = {2610.23100},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23100},
}
RIS
TY  - UNPB
TI  - Comparing word probabilities in finite groups
AU  - Lorenzo Putignano
AU  - Matteo Vannacci
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.23100
UR  - https://arxiv.org/abs/2610.23100
AB  - We use results from extremal graph theory and analysis to compare word probabilities in finite groups. In particular, we show that the probability of satisfying the 2-Engel word admits a positive lower bound in terms of the probability that an element has order dividing 3. More generally, using a group removal lemma, we obtain analogous bounds for x^m-good words.
ER  -