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Post by csdude07 on Nov 23, 2009 1:49:12 GMT -5
how funny is my sig? On a scale from 1-10, 1 being lame, 10 being ROFL funny.
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Post by cliff "woo" harris on Nov 23, 2009 1:49:15 GMT -5
GIVEN PROBLEM:
Let φ: G --> H be an isomorphism between groups G and H and let S be a subgroup of G. Prove that φ(S) is a subgroup of H.
notation: φ(S) = {h∈H: φ(x)=h for some x∈G}
My Solution:
So by the subgroup thrm., we need to show that φ(S) has an identity, inverses, and closure.
1. First we need to show that the identity of H is in φ(S)
Let h = eh for all h∈H
Then φ(eg) = eh
So the identity of H is in φ(S) .
2. Next we need to show that if a∈φ(S), then a-1∈φ(S)
No clue how to prove this, help?
3. Lastly, we must show that if a,b∈φ(S), then ab∈φ(S)
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Post by Spencer on Nov 23, 2009 1:49:16 GMT -5
LOL CHOSE NICE COMMUNICATION DUCKSTER amirite |
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Post by cliff "woo" harris on Nov 23, 2009 1:49:34 GMT -5
someone do that proof for me and I'll give you a free first.
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Post by ashes on Nov 23, 2009 1:49:39 GMT -5
Who would be in? Ashes lets quit basketball sims and do a college football sim. Ya college football and wrestling |
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Post by Clifford "Poop" Harris on Nov 23, 2009 1:49:46 GMT -5
What sucks about this thread is people are gonna think this is solely a post pad thread. It's a shame they won't get to see the detailed discussions in between.. we are witnesses... |
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Post by Spencer on Nov 23, 2009 1:49:50 GMT -5
GIVEN PROBLEM: Let φ: G --> H be an isomorphism between groups G and H and let S be a subgroup of G. Prove that φ(S) is a subgroup of H. notation: φ(S) = {h∈H: φ(x)=h for some x∈G} My Solution: So by the subgroup thrm., we need to show that φ(S) has an identity, inverses, and closure. 1. First we need to show that the identity of H is in φ(S) Let h = eh for all h∈H Then φ(eg) = eh So the identity of H is in φ(S) . 2. Next we need to show that if a∈φ(S), then a-1∈φ(S) No clue how to prove this, help? 3. Lastly, we must show that if a,b∈φ(S), then ab∈φ(S) I think I know the answer. Its a chip on Duckys shoulder. |
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Post by Clifford "Poop" Harris on Nov 23, 2009 1:50:01 GMT -5
how funny is my sig? On a scale from 1-10, 1 being lame, 10 being ROFL funny. negative 5 |
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Post by Trunks on Nov 23, 2009 1:50:06 GMT -5
fuck the grizzlies.. dick. everytime i try to rebuild they rebuild, and when i try to win they win.. FUCK THEM!
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Post by kobe24 on Nov 23, 2009 1:50:09 GMT -5
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Post by Spencer on Nov 23, 2009 1:50:13 GMT -5
Who would be in? Ashes lets quit basketball sims and do a college football sim. Ya college football and wrestling CFB would be sick though. |
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Post by cliff "woo" harris on Nov 23, 2009 1:50:19 GMT -5
LOL CHOSE NICE COMMUNICATION DUCKSTER lol I was typing fast since we are post padding.. |
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Post by Brophdog88 on Nov 23, 2009 1:50:28 GMT -5
Ducky, what page did the discussions go to
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Post by Spencer on Nov 23, 2009 1:50:35 GMT -5
I hate that college football sucks here.
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Post by Spencer on Nov 23, 2009 1:50:52 GMT -5
Actually The Big Game was sick.
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