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#1 2012-11-28 20:41:50

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

order of a cyclick group

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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#2 2012-11-30 00:57:14

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: order of a cyclick group

(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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