Groups of order 5: Difference between revisions

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{{groups of order|5}}
{{groups of order|5}}


There is, up to isomorphism, a unique group of order 5, namely [[cyclic group:Z5]]. This can be proved in many ways, including simply listing possible multiplication tables, but it also follows from the fact that 2 is a [[prime number]] and [[equivalence of definitions of group of prime order|there is a ''unique'' isomorphism class of group of prime order, namely that of the cyclic group of prime order]].
There is, up to isomorphism, a unique group of order 5, namely [[cyclic group:Z5]]. This can be proved in many ways, including simply listing possible multiplication tables, but it also follows from the fact that 5 is a [[prime number]] and [[equivalence of definitions of group of prime order|there is a ''unique'' isomorphism class of group of prime order, namely that of the cyclic group of prime order]].

Revision as of 20:45, 3 May 2013

This article gives information about, and links to more details on, groups of order 5
See pages on algebraic structures of order 5 | See pages on groups of a particular order

There is, up to isomorphism, a unique group of order 5, namely cyclic group:Z5. This can be proved in many ways, including simply listing possible multiplication tables, but it also follows from the fact that 5 is a prime number and there is a unique isomorphism class of group of prime order, namely that of the cyclic group of prime order.