报告题目：Conjugacy classes of normalsubgroups
I.It is known that the structure of a finite group is strongly controlledby the set of its conjugacy classes. Let G be a finite group and N a normal subgroup of G. Since N is union of conjugacy classes of G, it is natural to wonder what information on the structure of N can be obtained from the G-classes of N, that is, the conjugacy classes in G contained in N. Recent researches have put forward that the G-classes of a finite group also have influence on the structure of its normal subgroups. In this talk we analyze some properties relative to graphs associated to conjugacy G-classes of a normal subgroup N.
II. Let G be a finite group and N a normal subgroup of G. The main topic concerning this talk is the structure of N under certain conditions on its conjugacy G-class sizes. We would like to point out that there is no relation between the cardinal of the set of the conjugacy class sizes of N and the cardinal of the set of its G-class sizes. We present some results about the structure of normal subgroups with few G-class sizes. Moreover,we analyze structural properties of normal subgroups considering its G-class sizes of p-regular elements as well as its G-class sizes of prime-power order elements.