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  3. (a) show that a group that has only a finite numbe

(a) Show that a group that has only a finite number of subgroups must be a...

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Advance Math

(a) Show that a group that has only a finite number of subgroupsmust be a finite group.

(b) Let G be a group that has exactly one nontrivial, propersubgroup. Show that G must be isomorphic to Zp2 for some primenumber p. (Hint: use part (a) to conclude that G is finite. LetH

be the one nontrivial, proper subgroup of G. Start by showingthat G and hence H must be cyclic.)

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