Banca de DEFESA: Wállef Januário Pereira da Silva

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Wállef Januário Pereira da Silva
DATE: 11/11/2022
TIME: 14:00
LOCAL: Departamento de Matemática
TITLE: 
Soluble and Pronilpotent Groups with Engel's Conditions

KEY WORDS:
Engel Elements, Pronilpotent Groups, Soluble Groups.

PAGES: 76
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Álgebra
SPECIALTY: Álgebra Comutativa
SUMMARY:
Let G be a finitely generated pronilpotent group. In this work we consider the following conditions:

(*) For every x,y \in G there are positive integers n=n(x,y) and q=q(x,y) such that [x,{}_{n}y^{q}]=1;

(**) For every x,y \in G there are positive integers n=n(x,y) and q=q(x,y) such that [x^{q},{}_{ n}y]=1.

We show that if G satisfies (*) then G is a virtually nilpotent group. If G satisfies (**) then G is nilpotent. When G is a finitely generated soluble (abstract) group satisfying (*) or (**), we show that G is virtually nilpotent. This generalizes Gruenberg's theorem which says that every finitely generated soluble Engel group is nilpotent.

BANKING MEMBERS:
Externo à Instituição - CARMINE MONETTA
Interna - 1994292 - CRISTINA ACCIARRI
Interno - 1984613 - IGOR DOS SANTOS LIMA
Externo à Instituição - JHONE CALDEIRA SILVA - UFG
Presidente - 1224071 - PAVEL SHUMYATSKY
Notícia cadastrada em: 14/09/2022 10:40
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