Banca de DEFESA: Mateus Figueiredo de Souza

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Mateus Figueiredo de Souza
DATE: 14/03/2024
TIME: 14:00
LOCAL: Departamento de Matemática
TITLE:

On finite groups in which all commutators have prime power orders

KEY WORDS:

Fitting Height, Finite Groups, Turull Towers

PAGES: 66
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

The study of finite groups in which every element has prime power order (EPPO-groups) was initiated in pioneering works of G. Higman and M. Suzuki. Nowadays EPPO-groups are fairly well understood. For instance, it is known that if G is a finite soluble EPPO-group, then the Fitting height of G is at most 3 and |π(G)| ⩽ 2. Moreover, if G is insoluble, then the soluble radical R(G) of G is a 2-group and the quotient group G/R(G) belongs to a list of exactly 9 groups determined by Suzuki. In the present work we concentrate on finite groups in which every commutator has prime power order (CPPO- groups). Roughly, we show that if G is a finite CPPO-group, then the structure of G′ is similar to that of an EPPO-group. In particular, we show that the Fitting height of any finite soluble CPPO-group is at most 3 and |π(G′)| ⩽ 3. Moreover, if G is insoluble, then R(G′) is a 2-group and G′/R(G′) is isomorphic to a simple EPPO-group.

COMMITTEE MEMBERS:
Externo à Instituição - DANILO SANÇÃO DA SILVEIRA - UFOP
Interno - 1198222 - EMERSON FERREIRA DE MELO
Externo à Instituição - JHONE CALDEIRA SILVA - UFG
Presidente - 1224071 - PAVEL SHUMYATSKY
Interno - 1209688 - RAIMUNDO DE ARAUJO BASTOS JUNIOR