Banca de DEFESA: Sharmenya Jany Andrade Correia de Sousa

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : Sharmenya Jany Andrade Correia de Sousa
DATE: 09/02/2023
TIME: 14:30
LOCAL: PPGMAT
TITLE:

On the Classification of n-Centralizers Groups

KEY WORDS:

Centralizers of Elements. n-Centralizers Groups. Classification of Groups. 

PAGES: 83
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

Let G a group and denote by Cent(G) the set of all its centralizers of elements. We say that G is n-centralizer when |Cent(G)|= n. Of course, a group is 1-centralizer if, and only if, is abelian. Furthermore, does not exists 2 or 3-centralizers groups. A natural question is if fixed the size of Cent(G), if it is possible to obtain a characterization of the group G. In this work, based on articles of A. Abdollahi, S. M. J. Amiri, A. M. Hassanabadi [1] and M. Zarrin [29], we study and classify the n-centralizers groups for n \in {4,5,6,7,8}. In addition, we also study the paper of S. M. J. Amiri and H. Rostami [5], in which another approach was taken, in which, when considering the class of all non-abelian groups of a prefixed order, we classify the one that has the smallest number of centralizers.

BANKING MEMBERS:
Interno - 1601562 - ALEX CARRAZEDO DANTAS
Presidente - 1984613 - IGOR DOS SANTOS LIMA
Interno - 2255154 - MARTINO GARONZI
Externo à Instituição - MOHSEN AMIRI - UFAM