Powers in finite groups and a criterion for solubility

DOI10.1090/S0002-9939-2013-11790-9zbMath1320.20019MaRDI QIDQ2855896

Aner Shalev, Martin W. Liebeck

Publication date: 23 October 2013

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

zbMATH Keywords

finite groupssoclesWaring problemalmost simple groupssolubilityword mapspowers of elements

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Special subgroups (Frattini, Fitting, etc.) (20D25) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (3)

Power sets and soluble subgroups ⋮ On the number of elements that are not \(k\)th powers in a group. ⋮ On Engel words on simple algebraic groups.

Cites Work

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• Powerful \(p\)-groups. I: Finite groups.
• Prime power graphs for groups of Lie type
• Powers in Finitely Generated Groups
• Probability that an element of a finite group has a square root
• On Ree's Series of Simple Groups

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