Dear Rulin, > On 02 Feb 2017, at 12:45, Rulin Shen <shenru...@hotmail.com> wrote: > > Dear Prof. Cameron, > > Thanks for your answer. Sorry to my question's condition should be |H^c \cap > Hg|=|G|/4, where H^c the complement of H in G, and all g. So sorry!
Then the problem seems to become trivial: H^c \cap Hg either equals the empty set (when g\in H) or else Hg. By your condition, the former case must not occur for any g\neq 1, thus H must be trivial. But then |H^c \cap Hg|=1 for g\neq 1, thus |G|=4 and G is either C_4 or C_2 x C_2. Cheers, Max _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
