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Jan 12, 2013 at 7:35 comment added Mart @Wei Zhou: By the sizes of conjugacy classes of PGL the size of the conjugacy class of an order-k cyclic subgroup $C$ must be $q(q-1)$ or $q(q+1)$.
Jan 12, 2013 at 5:43 comment added Wei Zhou @Mart: Sorry I have no reference on PGL at hand. But I think $1/2$ come from $|G:N_G(C)|$.
Jan 12, 2013 at 3:27 history answered Wei Zhou CC BY-SA 3.0