Recent content by rulin

Let X = \{1,2,\cdots, p\} with p prime, and Y = \{1,2,\cdots,t,i_1,i_2,\cdots,i_{p - t}\} with 1\leq t\leq p - 1 and i_j\not\in X for 1\leq j\leq p - t. Supose that a and b are both p-rotation in X and Y, respectively. Whether or not p don't divide the order of ab?

the order of sylow p-subgroup of A_n is not hard to compute, but the one of normalizer of sylow p-subgroup, how to compute?

what is the order of normalizer of Sylow p-subgroup of simple groups A_n?

Maybe i don't know the order of the subgroup generated by P and Q, but this group satisfied above condition must be nilpotent.

A subgroup H of a group G is fully invariant if t(H)<=H for every endomorphism t of G. Let G is finite p-group has a fully invariant subgroup of order d for every d dividing |G|. What is the structure of G ?