Roberto Ialenti Dipartimento di Matematica e Applicazioni "Renato

Caccioppoli" Università degli Studi di Napoli "Federico II"

Día: Dijous 21d'abril de 2016,

Hora: 12:30hores

Lloc : Saló de Graus. Facultat de Matemàtiquess,

Resum: A subgroup H of a group G is said to be permutable if HK = KH for every subgroup K of G. In the theory of factorized groups, some problems may be studied making some assumptions on permutability connections between the factors. Starting from a result obtained by J. C. Beidleman and H. Heineken in the case of finite groups, in this talk I will discuss about the embedding properties of the commutator subgroups A' and B' in the infinite group G=AB, where A and B satsify a certain generalized condition of permutability, under suitable finiteness conditions on the rank of the group G. In recent years many authors studied groups, which are large in some sense, and the influence that large subgroups may have on the structure of the whole group. I will discuss about groups of infinite rank in which every subgroup of infinite rank satisies a certain generalized condition of permutability.