Profinite groups with an automorphism whose fixed points are right Engel
| Autor: | Cristina Acciarri, Evgeny Khukhro, Pavel Shumyatsky |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Profinite group
20E18 20E3 20F45 20F40 20D15 20F19 Coprime integers Group (mathematics) Applied Mathematics General Mathematics Locally nilpotent Group Theory (math.GR) Fixed point Automorphism Combinatorics FOS: Mathematics Element (category theory) Mathematics - Group Theory G110 Pure Mathematics Mathematics |
| Zdroj: | Proceedings of the American Mathematical Society. 147:3691-3703 |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | An element g g of a group G G is said to be right Engel if for every x ∈ G x\in G there is a number n = n ( g , x ) n=n(g,x) such that [ g , n x ] = 1 [g,{}_{n}x]=1 . We prove that if a profinite group G G admits a coprime automorphism φ \varphi of prime order such that every fixed point of φ \varphi is a right Engel element, then G G is locally nilpotent. |
| Databáze: | OpenAIRE |
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