Gaps in probabilities of satisfying some commutator-like identities

Costantino Delizia; Urban Jezernik; Primoz Moravec; Chiara Nicotera

Gaps in probabilities of satisfying some commutator-like identities

Group Theory 2019-02-12 v2

Authors: Costantino Delizia , Urban Jezernik , Primoz Moravec , Chiara Nicotera

Abstract

We show that there is a positive constant $\delta < 1$ such that the probability of satisfying either the $2$ -Engel identity $[X_1, X_2, X_2] = 1$ or the metabelian identity $[[X_1, X_2], [X_3, X_4]] = 1$ in a finite group is either $1$ or at most $\delta$ .

Keywords

finite groups commutator identities 2-Engel identity metabelian identity probability gap group theory

Cite

@article{arxiv.1809.02997,
  title  = {Gaps in probabilities of satisfying some commutator-like identities},
  author = {Costantino Delizia and Urban Jezernik and Primoz Moravec and Chiara Nicotera},
  journal= {arXiv preprint arXiv:1809.02997},
  year   = {2019}
}

Comments

23 pages; referees' comments, new Lemma 4.1.1, correcting and simplifying 4.4.2 and 4.6.2

Gaps in probabilities of satisfying some commutator-like identities

Abstract

Keywords

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