
Sylowp subgroups of A4
12=2^2*3..So i will have to list the Sylow2 subgroup of A4 whose cardinality will be 2^2=4 and Sylow3 subgroup whose cardinality will be 3.
one of the book that i refered said that there are 4 Sylow3 subgroups of cardinality 3 and 1 Sylow2 subgroup of cardinailty 4..
Can anyone please explain me this!

I got it!i need to use the fact that if np is the number of Sylowp subgroup of group G then np divides the index if P in G,(where Pis the Sylowp subgroup of G)..
So if P1 is the Sylow2 subgroup of A4 then np is either 1 or 3,where cardinality of P1 is 4..so there is only one Sylow2 subgroup of A4 as there are only three elements in A4 of order 2..(so these three elements along with identity form the only Sylow2 subgroup of A4)..
Similarly for Sylow3 subgroup of A4..The possibilty of np is 1or 2 or 4..nand then as above..
Correct??