Banca de DEFESA: Júlia Arêdes de Almeida

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Júlia Arêdes de Almeida
DATE: 12/02/2024
TIME: 10:00
LOCAL: a definir
TITLE:

Coverings and Pairwise Generation of some Primitive Groups of Wreath Product type

KEY WORDS:

Permutation group, Primitive group, Covering, Group generation.

PAGES: 80
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

The covering number of a finite noncyclic group G, denoted sigma(G), is the smallest positive integer k such that G is a union of k proper subgroups. If G is 2-generated, let omega(G) be the maximal size of a subset S of G with the property that any two distinct elements of S generate G. Since any proper subgroup of G can contain at most one element of such a set S, omega(G) is at most sigma(G). For a family of primitive groups G with a unique minimal normal subgroup N isomorphic to a direct power of the alternating group A_n and G/N cyclic, we calculate sigma(G) for n divisible by 6 and m at least 2. This is a generalization of a result of E. Swartz concerning the symmetric groups, which corresponds to the case m=1. For the above family of primitive groups G, we also prove a result concerning pairwise generation: for fixed m at least 2 and n even, we calculate asymptotically the value of omega(G) when n goes to infinity and show that omega(G)/sigma(G) tends to 1 as n tends to infinity.

COMMITTEE MEMBERS:
Externo à Instituição - FRANCESCO FUMAGALLI - UniFI
Interno - 1601562 - ALEX CARRAZEDO DANTAS
Externo à Instituição - CSABA SCHNEIDER - UFMG
Interno - 1198222 - EMERSON FERREIRA DE MELO
Presidente - 2255154 - MARTINO GARONZI