4) Assume that the following information is known: if G is a group and H, K are subgroups of G such that KsHSG, then [G:

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4 Assume That The Following Information Is Known If G Is A Group And H K Are Subgroups Of G Such That Kshsg Then G 1 (47.99 KiB) Viewed 23 times

4) Assume that the following information is known: if G is a group and H, K are subgroups of G such that KsHSG, then [G: K] = [G: H][H: K). Prove the following: 1) Let G be a group. If HSG, then |G| = [G : H][H. Il) Let G be a group and H, KSG such that HI= 186 and [K] = 31. Show that HNK = {ec} or else HO K = K. III) If G is a group of prime order, then G is cyclic.