Question

give an example of an non-cyclic gp which has all the proper subgroups cyclic?​

Answer 1

Answer:

The group U(8) = {1, 3, 5, 7} is noncyclic since 11 = 32 = 52 = 72 = 1 (so there are

no generators). The only proper subgroups are {1}, {1, 3}, {1, 5}, and {1, 7}, which

are all obviously cyclic.

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Answer 2

Answer:

Every non- cyclic group contains at least three cyclic subgroups of some order. arbitrary proper divisor of the order of the group. since G is non-cyclic and hence it has been proved that g cannot be divisible by more than two distinct prime numbers.

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