An upper bound for the nonsolvable length of a finite group in terms of its shortest law

DOI10.1112/plms.12476zbMath1522.20134arXiv2101.09119OpenAlexW3121809962MaRDI QIDQ6075040

Orazio Puglisi, Francesco Fumagalli, Felix Leinen

Publication date: 20 September 2023

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.09119

zbMATH Keywords

group lawfinite groupword mapnonsolvable length

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Other classes of groups defined by subgroup chains (20F22) General theory for finite permutation groups (20B05)

Related Items (3)

Coprime commutators and the nonsoluble length of a finite group ⋮ Strong conciseness of Engel words in profinite groups ⋮ Compact groups with probabilistically central monothetic subgroups

Cites Work

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• Nonsoluble and non-\(p\)-soluble length of finite groups.
• The Waring problem for finite simple groups.
• The Ore conjecture.
• The ubiquity of free subgroups in certain inverse limits of groups
• Words, permutations, and the nonsolvable length of a finite group
• A reduction theorem for nonsolvable finite groups
• Free subgroups of inverse limits of iterated wreath products of non-abelian finite simple groups in primitive actions
• Word maps and Waring type problems
• Varieties and simple groups
• Some Results and Problems in the Theory of Word Maps

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