On finite groups admitting automorphisms with nilpotent centralizers
| Autor: | Jhone Caldeira, Emerson de Melo |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0301 basic medicine
Discrete mathematics Normal subgroup Finite group Algebra and Number Theory Group (mathematics) Mathematics::Rings and Algebras 010102 general mathematics Automorphism 01 natural sciences Prime (order theory) Combinatorics Mathematics::Group Theory 03 medical and health sciences Nilpotent 030104 developmental biology Order (group theory) 0101 mathematics Nilpotent group Mathematics::Representation Theory Mathematics |
| Zdroj: | Journal of Algebra. 493:185-193 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2017.09.022 |
| Popis: | Let p be a prime. Let A be a finite group and M be a normal subgroup of A such that all elements in A ∖ M have order p. Suppose that A acts on a finite p ′ -group G in such a way that C G ( M ) = 1 . We show that if C G ( x ) is nilpotent for any x ∈ A ∖ M , then G is nilpotent. It is also proved that if A is a p-group and C G ( x ) is nilpotent of class at most c for any x ∈ A ∖ M , then the nilpotency class of G is bounded solely in terms of c and | A | . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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