Isomorphisms of finite groups

DgrayMan · **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.

Shadow · **Posted:** Mon, 26 Mar 2012 04:53:16 UTC

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.

DgrayMan · **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?

Shadow · **Posted:** Mon, 26 Mar 2012 05:54:19 UTC

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.

DgrayMan · **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

DgrayMan · **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!

Shadow · **Posted:** Tue, 27 Mar 2012 13:55:10 UTC

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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Isomorphisms of finite groups

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