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**princess snowwhite****Member**- Registered: 2012-11-06
- Posts: 29

Which of the following statements is false?

a>any abelian group of order 27 is cyclic

b>any abelian group of order 14 is cyclic

c>any abelian group of order 21 is cyclic

d>any abelian group of order 30 is cyclic

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

(a) is false. For example

is a non-cyclic Abelian group of order 27. It' s not cyclic because every non-identity element has order 3.

*Last edited by scientia (2012-11-30 00:57:51)*

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