- #1

Entropee

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How would I construct noncyclic groups of whatever order I want? For example g is order 8.

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- Thread starter Entropee
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- #1

Entropee

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How would I construct noncyclic groups of whatever order I want? For example g is order 8.

- #2

Office_Shredder

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http://en.wikipedia.org/wiki/List_of_small_groups

in which only a single noncyclic odd group is given, Z

- #3

lavinia

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How would I construct noncyclic groups of whatever order I want? For example g is order 8.

a group of prime order must be cyclic

if the order is nxm can you think of an example?

- #4

Entropee

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- #5

pasmith

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[itex]C_5 \times C_5[/itex] is an abelian group of order 25 in which every element other than the identity is of order 5.

([itex]C_n \times C_m[/itex] is not isomorphic to [itex]C_{n+m}[/itex] unless [itex]n[/itex] and [itex]m[/itex] are coprime.)

- #6

lavinia

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here is a group of order 6.

b[itex]^{3}[/itex] = a[itex]^{2}[/itex] = id

aba[itex]^{-1}[/itex] = b[itex]^{2}[/itex]

Try to show that every group of order 15 is abelian.

b[itex]^{3}[/itex] = a[itex]^{2}[/itex] = id

aba[itex]^{-1}[/itex] = b[itex]^{2}[/itex]

Try to show that every group of order 15 is abelian.

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