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The influence of class sizes on normal subgroups
It is known that the structure of a finite group is strongly controlled by the set of its conjugacy class sizes. Let G be a finite group and N be a normal subgroup of G. Since N is a union of conjugacy classes of G, it is natural to wonder what information on the structure of N can be obtained from the G-class sizes of N, that is, the sizes of the conjugacy classes of G contained in N. We would like to point out that there is no relation between the cardinal of the set of conjugacy class sizes of N and the cardinal of the set of its G-class sizes. However, several researches have put forward that the G-class sizes of a finite group also influence the structure of its normal subgroups. We present some recent results concerning this topic.
- Speaker
- Maria Jose Felipe (Universidad Politecnica de Valencia)