Property of isomorphism [closed]
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Let $phi $ be an isomorphism from G onto a group G'.Then For any element prove a and b in G, a and b commute if and only if $phi(a) $and $phi (b)$ commute.
abstract-algebra group-theory group-isomorphism
edited Nov 27 at 9:38
Arthur
110k7104186
asked Nov 27 at 9:31
Ameesha Yadav
12
closed as off-topic by Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D. Nov 27 at 14:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D.
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
-1
down vote
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Let $phi $ be an isomorphism from G onto a group G'.Then For any element prove a and b in G, a and b commute if and only if $phi(a) $and $phi (b)$ commute.
abstract-algebra group-theory group-isomorphism
edited Nov 27 at 9:38
Arthur
110k7104186
asked Nov 27 at 9:31
Ameesha Yadav
12
closed as off-topic by Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D. Nov 27 at 14:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D.
If this question can be reworded to fit the rules in the help center, please edit the question.
Is $phi$ an isomorphism? From which group to which group? (One needs to be precice about these things, because only then can one actually prove anything.) Also, what have you tried? You must have made some attempts before you decided to go through the process of registering here and posting the question. Please edit your post and tell us exactly where you're stuck. And if you say you have no idea to even begin, then I won't believe you.
– Arthur
Nov 27 at 9:32
I corrected my question.
– Ameesha Yadav
Nov 27 at 9:44
Please do not repeat your questions. It has been answered in the comments there already.
– Dietrich Burde
Nov 27 at 9:54
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Let $phi $ be an isomorphism from G onto a group G'.Then For any element prove a and b in G, a and b commute if and only if $phi(a) $and $phi (b)$ commute.
abstract-algebra group-theory group-isomorphism
edited Nov 27 at 9:38
Arthur
110k7104186
asked Nov 27 at 9:31
Ameesha Yadav
12
Let $phi $ be an isomorphism from G onto a group G'.Then For any element prove a and b in G, a and b commute if and only if $phi(a) $and $phi (b)$ commute.
abstract-algebra group-theory group-isomorphism
abstract-algebra group-theory group-isomorphism
edited Nov 27 at 9:38
Arthur
110k7104186
asked Nov 27 at 9:31
Ameesha Yadav
12
edited Nov 27 at 9:38
Arthur
110k7104186
asked Nov 27 at 9:31
Ameesha Yadav
12
edited Nov 27 at 9:38
Arthur
110k7104186
edited Nov 27 at 9:38
Arthur
110k7104186
edited Nov 27 at 9:38
Arthur
110k7104186
110k7104186
asked Nov 27 at 9:31
Ameesha Yadav
12
asked Nov 27 at 9:31
Ameesha Yadav
12
asked Nov 27 at 9:31
Ameesha Yadav
12
12
closed as off-topic by Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D. Nov 27 at 14:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D.
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D. Nov 27 at 14:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jendrik Stelzner, Christopher, Dietrich Burde, user302797, Arnaud D.
If this question can be reworded to fit the rules in the help center, please edit the question.
Is $phi$ an isomorphism? From which group to which group? (One needs to be precice about these things, because only then can one actually prove anything.) Also, what have you tried? You must have made some attempts before you decided to go through the process of registering here and posting the question. Please edit your post and tell us exactly where you're stuck. And if you say you have no idea to even begin, then I won't believe you.
– Arthur
Nov 27 at 9:32
I corrected my question.
– Ameesha Yadav
Nov 27 at 9:44
Please do not repeat your questions. It has been answered in the comments there already.
– Dietrich Burde
Nov 27 at 9:54
add a comment |
Is $phi$ an isomorphism? From which group to which group? (One needs to be precice about these things, because only then can one actually prove anything.) Also, what have you tried? You must have made some attempts before you decided to go through the process of registering here and posting the question. Please edit your post and tell us exactly where you're stuck. And if you say you have no idea to even begin, then I won't believe you.
– Arthur
Nov 27 at 9:32
I corrected my question.
– Ameesha Yadav
Nov 27 at 9:44
Please do not repeat your questions. It has been answered in the comments there already.
– Dietrich Burde
Nov 27 at 9:54
Is $phi$ an isomorphism? From which group to which group? (One needs to be precice about these things, because only then can one actually prove anything.) Also, what have you tried? You must have made some attempts before you decided to go through the process of registering here and posting the question. Please edit your post and tell us exactly where you're stuck. And if you say you have no idea to even begin, then I won't believe you.
– Arthur
Nov 27 at 9:32
Is $phi$ an isomorphism? From which group to which group? (One needs to be precice about these things, because only then can one actually prove anything.) Also, what have you tried? You must have made some attempts before you decided to go through the process of registering here and posting the question. Please edit your post and tell us exactly where you're stuck. And if you say you have no idea to even begin, then I won't believe you.
– Arthur
Nov 27 at 9:32
I corrected my question.
– Ameesha Yadav
Nov 27 at 9:44
I corrected my question.
– Ameesha Yadav
Nov 27 at 9:44
Please do not repeat your questions. It has been answered in the comments there already.
– Dietrich Burde
Nov 27 at 9:54
Please do not repeat your questions. It has been answered in the comments there already.
– Dietrich Burde
Nov 27 at 9:54
add a comment |
1 Answer
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Welcome to MSE! An isomorphism is merely a relabeling of the elements. Here, let $a,bin G$. Then we have $phi(ab) = phi(a)phi(b)$ and $phi(ba)=phi(b)phi(a)$. So $a,b$ commute if and only if $phi(a)phi(b)$ commute.
answered Nov 27 at 9:58
Wuestenfux
3,0951410
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Welcome to MSE! An isomorphism is merely a relabeling of the elements. Here, let $a,bin G$. Then we have $phi(ab) = phi(a)phi(b)$ and $phi(ba)=phi(b)phi(a)$. So $a,b$ commute if and only if $phi(a)phi(b)$ commute.
answered Nov 27 at 9:58
Wuestenfux
3,0951410
add a comment |
up vote
1
down vote
Welcome to MSE! An isomorphism is merely a relabeling of the elements. Here, let $a,bin G$. Then we have $phi(ab) = phi(a)phi(b)$ and $phi(ba)=phi(b)phi(a)$. So $a,b$ commute if and only if $phi(a)phi(b)$ commute.
answered Nov 27 at 9:58
Wuestenfux
3,0951410
add a comment |
up vote
1
down vote
up vote
1
down vote
Welcome to MSE! An isomorphism is merely a relabeling of the elements. Here, let $a,bin G$. Then we have $phi(ab) = phi(a)phi(b)$ and $phi(ba)=phi(b)phi(a)$. So $a,b$ commute if and only if $phi(a)phi(b)$ commute.
answered Nov 27 at 9:58
Wuestenfux
3,0951410
Welcome to MSE! An isomorphism is merely a relabeling of the elements. Here, let $a,bin G$. Then we have $phi(ab) = phi(a)phi(b)$ and $phi(ba)=phi(b)phi(a)$. So $a,b$ commute if and only if $phi(a)phi(b)$ commute.
answered Nov 27 at 9:58
Wuestenfux
3,0951410
answered Nov 27 at 9:58
Wuestenfux
3,0951410
answered Nov 27 at 9:58
Wuestenfux
3,0951410
answered Nov 27 at 9:58
Wuestenfux
3,0951410
3,0951410
add a comment |
add a comment |
Is $phi$ an isomorphism? From which group to which group? (One needs to be precice about these things, because only then can one actually prove anything.) Also, what have you tried? You must have made some attempts before you decided to go through the process of registering here and posting the question. Please edit your post and tell us exactly where you're stuck. And if you say you have no idea to even begin, then I won't believe you.
– Arthur
Nov 27 at 9:32
I corrected my question.
– Ameesha Yadav
Nov 27 at 9:44
Please do not repeat your questions. It has been answered in the comments there already.
– Dietrich Burde
Nov 27 at 9:54