If H is a Sylow p- subgroup of G with |G|= qn and q> n is a prime. Then H may be normal. O O True False
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- True or False Label each of the following statements as either true or false. 8. The set of all odd permutations in is a subgroup of .19. With and as in Exercise 18, prove that is a subgroup of . Exercise18: 18. If is a subgroup of , and is a normal subgroup of , prove that .Show that An has index 2 in Sn, and thereby conclude that An is always a normal subgroup of Sn.
- With H and K as in Exercise 18, prove that K is a normal subgroup of HK. Exercise18: If H is a subgroup of G, and K is a normal subgroup of G, prove that HK=KH.True or False Label each of the following statements as either true or false. 4. If a subgroup of a group is cyclic, then must be cyclic.18. If is a subgroup of the group such that for all left cosets and of in, prove that is normal in.