Let C be a class of groups, let G be a group and A, B two subgroups of G. We will say that A and B are C-connected if for all element a and b belonging respectively to A and B, the group < a, b > is in the class C. In particular we will focus on N-connection, where N is the class of nilpotent groups. Moreover, G is said to be the product of A and B, i.e. G=AB, if and only if for all element g in G, there exists a in A and b in B such that g=ab. In this thesis, given G=AB where A and B are N-connected subgroups, we discuss how some properties of the subgroups A and B can influence the structure of the whole group G.
Nilpotence relations in products of groups / Giulio Francalanci. - (2020).
Nilpotence relations in products of groups
Giulio Francalanci
2020
Abstract
Let C be a class of groups, let G be a group and A, B two subgroups of G. We will say that A and B are C-connected if for all element a and b belonging respectively to A and B, the group < a, b > is in the class C. In particular we will focus on N-connection, where N is the class of nilpotent groups. Moreover, G is said to be the product of A and B, i.e. G=AB, if and only if for all element g in G, there exists a in A and b in B such that g=ab. In this thesis, given G=AB where A and B are N-connected subgroups, we discuss how some properties of the subgroups A and B can influence the structure of the whole group G.File | Dimensione | Formato | |
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