- #1
metapuff
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A group is said to be indecomposable if it cannot be written as a product of smaller groups. An example of this is any group of prime order p, which is isomorphic to the group of integers modulo p (with addition as the group operation). Since the integers modulo p is a cyclic group (generated by 1), we have that any indecomposable group of prime order is cyclic. I have two questions:
Are ALL indecomposable groups cyclic? (N.B. not just those of prime order)
Are all cyclic groups indecomposable?
Thanks!
Are ALL indecomposable groups cyclic? (N.B. not just those of prime order)
Are all cyclic groups indecomposable?
Thanks!