What's the point of studying isomorphisms?
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I'm trying to learn about groups/rings and the concept of isomorphisms appears everywhere. I understand that an isomorphism between groups/rings shows that arithmetic in both structures is essentially the same, but I don't understand how this can be applied to deduce anything about them. If someone could give an example or explain how isomorphisms can be used to answer a question I'd greatly appreciate it.
group-isomorphism ring-isomorphism
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
$endgroup$
add a comment |
$begingroup$
I'm trying to learn about groups/rings and the concept of isomorphisms appears everywhere. I understand that an isomorphism between groups/rings shows that arithmetic in both structures is essentially the same, but I don't understand how this can be applied to deduce anything about them. If someone could give an example or explain how isomorphisms can be used to answer a question I'd greatly appreciate it.
group-isomorphism ring-isomorphism
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
$endgroup$
3
$begingroup$
An example maybe is that the Mobius transformation is isomorphic to the projective linear group as in math.stackexchange.com/questions/1055559/…. This reduces asking about a geometric transformation to something that can be done with complex matrices, which is more concrete.
$endgroup$
– twnly
Dec 29 '18 at 5:49
add a comment |
$begingroup$
I'm trying to learn about groups/rings and the concept of isomorphisms appears everywhere. I understand that an isomorphism between groups/rings shows that arithmetic in both structures is essentially the same, but I don't understand how this can be applied to deduce anything about them. If someone could give an example or explain how isomorphisms can be used to answer a question I'd greatly appreciate it.
group-isomorphism ring-isomorphism
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
$endgroup$
I'm trying to learn about groups/rings and the concept of isomorphisms appears everywhere. I understand that an isomorphism between groups/rings shows that arithmetic in both structures is essentially the same, but I don't understand how this can be applied to deduce anything about them. If someone could give an example or explain how isomorphisms can be used to answer a question I'd greatly appreciate it.
group-isomorphism ring-isomorphism
group-isomorphism ring-isomorphism
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
asked Dec 29 '18 at 5:42
uhhhhidkuhhhhidk
1216
1216
3
$begingroup$
An example maybe is that the Mobius transformation is isomorphic to the projective linear group as in math.stackexchange.com/questions/1055559/…. This reduces asking about a geometric transformation to something that can be done with complex matrices, which is more concrete.
$endgroup$
– twnly
Dec 29 '18 at 5:49
add a comment |
3
$begingroup$
An example maybe is that the Mobius transformation is isomorphic to the projective linear group as in math.stackexchange.com/questions/1055559/…. This reduces asking about a geometric transformation to something that can be done with complex matrices, which is more concrete.
$endgroup$
– twnly
Dec 29 '18 at 5:49
3
3
$begingroup$
An example maybe is that the Mobius transformation is isomorphic to the projective linear group as in math.stackexchange.com/questions/1055559/…. This reduces asking about a geometric transformation to something that can be done with complex matrices, which is more concrete.
$endgroup$
– twnly
Dec 29 '18 at 5:49
$begingroup$
An example maybe is that the Mobius transformation is isomorphic to the projective linear group as in math.stackexchange.com/questions/1055559/…. This reduces asking about a geometric transformation to something that can be done with complex matrices, which is more concrete.
$endgroup$
– twnly
Dec 29 '18 at 5:49
add a comment |
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$begingroup$
An example maybe is that the Mobius transformation is isomorphic to the projective linear group as in math.stackexchange.com/questions/1055559/…. This reduces asking about a geometric transformation to something that can be done with complex matrices, which is more concrete.
$endgroup$
– twnly
Dec 29 '18 at 5:49