Finding all of the element in a product group
I would like to find all of the element in the following group: $U_ntimes mathbb Z_n$ when $U_n$ is the Multiplicative group of integers modulo $n$ and $mathbb{Z}_n$ is the Sum group of integers modulo.
For example, How can I find part or all of the element in $U_{10}timesmathbb{Z}_{10}$?
group-theory
asked Dec 1 '18 at 20:21
vesii
856
add a comment |
I would like to find all of the element in the following group: $U_ntimes mathbb Z_n$ when $U_n$ is the Multiplicative group of integers modulo $n$ and $mathbb{Z}_n$ is the Sum group of integers modulo.
For example, How can I find part or all of the element in $U_{10}timesmathbb{Z}_{10}$?
group-theory
asked Dec 1 '18 at 20:21
vesii
856
What is your definition of the direct product? Tuples with componentwise group operation or via the universal property?
– Luke
Dec 1 '18 at 20:44
@Luke thanks for the reply. The definition is $Gtimes H = {(g,h)|gin G,hin H}$
– vesii
Dec 1 '18 at 21:05
That is a set, and not yet a group. How is the multiplication defined?
– Luke
Dec 1 '18 at 21:06
add a comment |
I would like to find all of the element in the following group: $U_ntimes mathbb Z_n$ when $U_n$ is the Multiplicative group of integers modulo $n$ and $mathbb{Z}_n$ is the Sum group of integers modulo.
For example, How can I find part or all of the element in $U_{10}timesmathbb{Z}_{10}$?
group-theory
asked Dec 1 '18 at 20:21
vesii
856
I would like to find all of the element in the following group: $U_ntimes mathbb Z_n$ when $U_n$ is the Multiplicative group of integers modulo $n$ and $mathbb{Z}_n$ is the Sum group of integers modulo.
For example, How can I find part or all of the element in $U_{10}timesmathbb{Z}_{10}$?
group-theory
group-theory
asked Dec 1 '18 at 20:21
vesii
856
asked Dec 1 '18 at 20:21
vesii
856
asked Dec 1 '18 at 20:21
vesii
856
asked Dec 1 '18 at 20:21
vesii
856
asked Dec 1 '18 at 20:21
vesii
856
856
What is your definition of the direct product? Tuples with componentwise group operation or via the universal property?
– Luke
Dec 1 '18 at 20:44
@Luke thanks for the reply. The definition is $Gtimes H = {(g,h)|gin G,hin H}$
– vesii
Dec 1 '18 at 21:05
That is a set, and not yet a group. How is the multiplication defined?
– Luke
Dec 1 '18 at 21:06
add a comment |
What is your definition of the direct product? Tuples with componentwise group operation or via the universal property?
– Luke
Dec 1 '18 at 20:44
@Luke thanks for the reply. The definition is $Gtimes H = {(g,h)|gin G,hin H}$
– vesii
Dec 1 '18 at 21:05
That is a set, and not yet a group. How is the multiplication defined?
– Luke
Dec 1 '18 at 21:06
What is your definition of the direct product? Tuples with componentwise group operation or via the universal property?
– Luke
Dec 1 '18 at 20:44
What is your definition of the direct product? Tuples with componentwise group operation or via the universal property?
– Luke
Dec 1 '18 at 20:44
@Luke thanks for the reply. The definition is $Gtimes H = {(g,h)|gin G,hin H}$
– vesii
Dec 1 '18 at 21:05
@Luke thanks for the reply. The definition is $Gtimes H = {(g,h)|gin G,hin H}$
– vesii
Dec 1 '18 at 21:05
That is a set, and not yet a group. How is the multiplication defined?
– Luke
Dec 1 '18 at 21:06
That is a set, and not yet a group. How is the multiplication defined?
– Luke
Dec 1 '18 at 21:06
add a comment |
1 Answer
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$U_{10}oplus mathbb Z_{10}cong mathbb Z_{4}oplus mathbb Z_{10}$
Can you do now?
answered Dec 2 '18 at 15:01
Shubham
1,5851519
add a comment |
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1 Answer
1
active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$U_{10}oplus mathbb Z_{10}cong mathbb Z_{4}oplus mathbb Z_{10}$
Can you do now?
answered Dec 2 '18 at 15:01
Shubham
1,5851519
add a comment |
$U_{10}oplus mathbb Z_{10}cong mathbb Z_{4}oplus mathbb Z_{10}$
Can you do now?
answered Dec 2 '18 at 15:01
Shubham
1,5851519
add a comment |
$U_{10}oplus mathbb Z_{10}cong mathbb Z_{4}oplus mathbb Z_{10}$
Can you do now?
answered Dec 2 '18 at 15:01
Shubham
1,5851519
$U_{10}oplus mathbb Z_{10}cong mathbb Z_{4}oplus mathbb Z_{10}$
Can you do now?
answered Dec 2 '18 at 15:01
Shubham
1,5851519
answered Dec 2 '18 at 15:01
Shubham
1,5851519
answered Dec 2 '18 at 15:01
Shubham
1,5851519
answered Dec 2 '18 at 15:01
Shubham
1,5851519
1,5851519
add a comment |
add a comment |
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What is your definition of the direct product? Tuples with componentwise group operation or via the universal property?
– Luke
Dec 1 '18 at 20:44
@Luke thanks for the reply. The definition is $Gtimes H = {(g,h)|gin G,hin H}$
– vesii
Dec 1 '18 at 21:05
That is a set, and not yet a group. How is the multiplication defined?
– Luke
Dec 1 '18 at 21:06