[GAP Forum] A question of GAP
Max Horn
max at quendi.de
Thu Feb 2 16:31:06 GMT 2017
Dear Rulin,
> On 02 Feb 2017, at 12:45, Rulin Shen <shenrulin at 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
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