Hi,

whcih of the following groups would be isomorphic?

D32

A5

D22

A22

A32

S32

S22

Z60

S60

A60.

thanks

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- Jul 12th 2007, 08:55 AM #1

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- Jul 12th 2007, 09:37 AM #2

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64 elements

A5

D22

A22

A32

S32

S22

Z60

S60

A60.

The only ones that have a chance of being isomorphic are A5 and Z60. But A5 is non-abelian and Z60 is. So there is no isomorphism here.

- Jul 12th 2007, 10:22 AM #3

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- Jul 12th 2007, 01:23 PM #4

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$\displaystyle 2^{\aleph_0}$

Z4 x Z3 x Z5

D11 x Z2

Z4 x Z8

S22

Z60

A5

A22

A32

S32

A60

S60

The only possible ones are:

Z4xZ3xZ5 and Z60 and A5

We note the first two are abelian and third one is not.

Thus, it remains to show that the first two are or not isomorphic.

Indeed they are because 4,3,5 in Z4xZ3xZ5 are relatively prime.