If H and K are subgroups of G of order 75 and 242 respectively, what can you say about H N K?
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- 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 .Suppose G1 and G2 are groups with normal subgroups H1 and H2, respectively, and with G1/H1 isomorphic to G2/H2. Determine the possible orders of H1 and H2 under the following conditions. a. G1=24 and G2=18 b. G1=32 and G2=40With 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.