Paper 3, Section II, D

Groups | Part IA, 2010

Let GG be a finite group, XX the set of proper subgroups of GG. Show that conjugation defines an action of GG on XX.

Let BB be a proper subgroup of GG. Show that the orbit of GG on XX containing BB has size at most the index G:B|G: B|. Show that there exists a gGg \in G which is not conjugate to an element of BB.

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