Mixing
Isomorphism relation in $Hom(mathbb{Z}_6,mathbb{R}^*oplusmathbb{C}^*)?$
0
$begingroup$
Let $mathbb{R}^*$ and $mathbb{C}^*$ are multiplicative group of real number and complex number relatively.
what group does isomorphism with
$$Hom(mathbb{Z}_6,mathbb{R}^*oplusmathbb{C}^*)?$$
group-theory abelian-groups group-homomorphism
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
$endgroup$
|
show 1 more comment
0
$begingroup$
Let $mathbb{R}^*$ and $mathbb{C}^*$ are multiplicative group of real number and complex number relatively.
what group does isomorphism with
$$Hom(mathbb{Z}_6,mathbb{R}^*oplusmathbb{C}^*)?$$
group-theory abelian-groups group-homomorphism
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
$endgroup$
2
$begingroup$
Hint: the image of $0inmathbb{Z}_6$ must be an element of order divisor of 6. In $mathbb{R}^*$ there are only two such elements and in $mathbb{C}^*$ there are the six-th roots of unity.
$endgroup$
– Javi
Jan 20 at 11:50
1
$begingroup$
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
$endgroup$
– Shaun
Jan 20 at 14:26
$begingroup$
@Javi Surely you meant the image of $1$, not $0$?
$endgroup$
– David C. Ullrich
Jan 20 at 17:39
$begingroup$
@DavidC.Ullrich absolutely, I guess I didn't know what I was typing
$endgroup$
– Javi
Jan 20 at 21:27
$begingroup$
Does $mathbb{C}^* $ have six roots at this state? So the answer is group with 12 elements?
$endgroup$
– Ruhi. Js
Jan 22 at 10:00
|
show 1 more comment
0
0
0
$begingroup$
Let $mathbb{R}^*$ and $mathbb{C}^*$ are multiplicative group of real number and complex number relatively.
what group does isomorphism with
$$Hom(mathbb{Z}_6,mathbb{R}^*oplusmathbb{C}^*)?$$
group-theory abelian-groups group-homomorphism
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
$endgroup$
Let $mathbb{R}^*$ and $mathbb{C}^*$ are multiplicative group of real number and complex number relatively.
what group does isomorphism with
$$Hom(mathbb{Z}_6,mathbb{R}^*oplusmathbb{C}^*)?$$
group-theory abelian-groups group-homomorphism
group-theory abelian-groups group-homomorphism
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
edited Jan 22 at 10:06
Ruhi. Js
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
asked Jan 20 at 11:37
Ruhi. JsRuhi. Js
64
64
2
$begingroup$
Hint: the image of $0inmathbb{Z}_6$ must be an element of order divisor of 6. In $mathbb{R}^*$ there are only two such elements and in $mathbb{C}^*$ there are the six-th roots of unity.
$endgroup$
– Javi
Jan 20 at 11:50
1
$begingroup$
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
$endgroup$
– Shaun
Jan 20 at 14:26
$begingroup$
@Javi Surely you meant the image of $1$, not $0$?
$endgroup$
– David C. Ullrich
Jan 20 at 17:39
$begingroup$
@DavidC.Ullrich absolutely, I guess I didn't know what I was typing
$endgroup$
– Javi
Jan 20 at 21:27
$begingroup$
Does $mathbb{C}^* $ have six roots at this state? So the answer is group with 12 elements?
$endgroup$
– Ruhi. Js
Jan 22 at 10:00
|
show 1 more comment
2
$begingroup$
Hint: the image of $0inmathbb{Z}_6$ must be an element of order divisor of 6. In $mathbb{R}^*$ there are only two such elements and in $mathbb{C}^*$ there are the six-th roots of unity.
$endgroup$
– Javi
Jan 20 at 11:50
1
$begingroup$
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
$endgroup$
– Shaun
Jan 20 at 14:26
$begingroup$
@Javi Surely you meant the image of $1$, not $0$?
$endgroup$
– David C. Ullrich
Jan 20 at 17:39
$begingroup$
@DavidC.Ullrich absolutely, I guess I didn't know what I was typing
$endgroup$
– Javi
Jan 20 at 21:27
$begingroup$
Does $mathbb{C}^* $ have six roots at this state? So the answer is group with 12 elements?
$endgroup$
– Ruhi. Js
Jan 22 at 10:00
2
2
$begingroup$
Hint: the image of $0inmathbb{Z}_6$ must be an element of order divisor of 6. In $mathbb{R}^*$ there are only two such elements and in $mathbb{C}^*$ there are the six-th roots of unity.
$endgroup$
– Javi
Jan 20 at 11:50
$begingroup$
Hint: the image of $0inmathbb{Z}_6$ must be an element of order divisor of 6. In $mathbb{R}^*$ there are only two such elements and in $mathbb{C}^*$ there are the six-th roots of unity.
$endgroup$
– Javi
Jan 20 at 11:50
1
1
$begingroup$
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
$endgroup$
– Shaun
Jan 20 at 14:26
$begingroup$
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
$endgroup$
– Shaun
Jan 20 at 14:26
$begingroup$
@Javi Surely you meant the image of $1$, not $0$?
$endgroup$
– David C. Ullrich
Jan 20 at 17:39
$begingroup$
@Javi Surely you meant the image of $1$, not $0$?
$endgroup$
– David C. Ullrich
Jan 20 at 17:39
$begingroup$
@DavidC.Ullrich absolutely, I guess I didn't know what I was typing
$endgroup$
– Javi
Jan 20 at 21:27
$begingroup$
@DavidC.Ullrich absolutely, I guess I didn't know what I was typing
$endgroup$
– Javi
Jan 20 at 21:27
$begingroup$
Does $mathbb{C}^* $ have six roots at this state? So the answer is group with 12 elements?
$endgroup$
– Ruhi. Js
Jan 22 at 10:00
$begingroup$
Does $mathbb{C}^* $ have six roots at this state? So the answer is group with 12 elements?
$endgroup$
– Ruhi. Js
Jan 22 at 10:00
|
show 1 more comment
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2
$begingroup$
Hint: the image of $0inmathbb{Z}_6$ must be an element of order divisor of 6. In $mathbb{R}^*$ there are only two such elements and in $mathbb{C}^*$ there are the six-th roots of unity.
$endgroup$
– Javi
Jan 20 at 11:50
1
$begingroup$
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
$endgroup$
– Shaun
Jan 20 at 14:26
$begingroup$
@Javi Surely you meant the image of $1$, not $0$?
$endgroup$
– David C. Ullrich
Jan 20 at 17:39
$begingroup$
@DavidC.Ullrich absolutely, I guess I didn't know what I was typing
$endgroup$
– Javi
Jan 20 at 21:27
$begingroup$
Does $mathbb{C}^* $ have six roots at this state? So the answer is group with 12 elements?
$endgroup$
– Ruhi. Js
Jan 22 at 10:00