On the Exponent of a Verbal Subgroup in a Finite Group

2012/06/19 by Pavel Shumyatsky, Shumyatsky, Pavel
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1206.4353

Accepted for publication in the Journal of the Australian Mathematical Society

arxiv created 2012/06/19 · openalex publication_date 2012/06/19 · arxiv updated 2012/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let w be a multilinear commutator word. We prove that if e is a positive integer and G is a finite group in which any nilpotent subgroup generated by w-values has exponent dividing e then the exponent of the corresponding verbal subgroup w(G) is bounded in terms of e and w only.

Related

• Bounding the Exponent of a Verbal Subgroup
• Words and pronilpotent subgroups in profinite groups
• On conciseness of words in profinite groups
• On countable coverings of word values in profinite groups
• A nilpotency criterion for some verbal subgroups