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 Post subject: Isomorphisms of finite groupsPosted: Mon, 26 Mar 2012 03:27:37 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
So i made a group table. Both are not abelian, and i don't think they're cyclic, so how do i show if they are or are not an isomorphism.

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 Post subject: Re: Isomorphisms of finite groupsPosted: Mon, 26 Mar 2012 04:53:16 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
DgrayMan wrote:
So i made a group table. Both are not abelian, and i don't think they're cyclic, so how do i show if they are or are not an isomorphism.

? All cyclic groups are abelian....

In any case, check out the elements of order 4, and try rearranging your tables to match those with one another.

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 Post subject: Re: Isomorphisms of finite groupsPosted: Mon, 26 Mar 2012 05:36:40 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
what do you mean elements of order 4? and how do i find those out? and how should i rearrange the table? what am i trying to match up?

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 Post subject: Re: Isomorphisms of finite groupsPosted: Mon, 26 Mar 2012 05:54:19 UTC
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DgrayMan wrote:
what do you mean elements of order 4? and how do i find those out? and how should i rearrange the table? what am i trying to match up?

Look along your diagonal, those are the squares, and only two elements don't square to I, but they square to elements which DO square to I, so they have order 4.

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 Post subject: Re: Isomorphisms of finite groupsPosted: Mon, 26 Mar 2012 16:59:29 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
yea im confused as hell. so i think im gonna bite the bullet on this one

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 Post subject: Re: Isomorphisms of finite groupsPosted: Tue, 27 Mar 2012 04:54:19 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
I lied! i didn't give up and i found out that there are some elements in G each group that do not have the same order as other elements in H!

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 Post subject: Re: Isomorphisms of finite groupsPosted: Tue, 27 Mar 2012 13:55:10 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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DgrayMan wrote:
I lied! i didn't give up and i found out that there are some elements in G each group that do not have the same order as other elements in H!

You didn't lie then, "bite the bullet" means get down to serious work.

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