Mixing
Is the following cyclic group test wrong in WolframAlpha?
Please see here
Cyclic group test
Isn't this a mistake? Isn't this a cyclic group generated by $(5,1)$ ? thank you!
group-theory cyclic-groups direct-product
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
asked Nov 22 '18 at 0:48
LoliLoli
342310
add a comment |
Please see here
Cyclic group test
Isn't this a mistake? Isn't this a cyclic group generated by $(5,1)$ ? thank you!
group-theory cyclic-groups direct-product
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
asked Nov 22 '18 at 0:48
LoliLoli
342310
no one knows? :(
– Loli
Nov 22 '18 at 1:07
Try posting this on mathematica.se.
– rogerl
Nov 22 '18 at 2:27
add a comment |
Please see here
Cyclic group test
Isn't this a mistake? Isn't this a cyclic group generated by $(5,1)$ ? thank you!
group-theory cyclic-groups direct-product
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
asked Nov 22 '18 at 0:48
LoliLoli
342310
Please see here
Cyclic group test
Isn't this a mistake? Isn't this a cyclic group generated by $(5,1)$ ? thank you!
group-theory cyclic-groups direct-product
group-theory cyclic-groups direct-product
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
asked Nov 22 '18 at 0:48
LoliLoli
342310
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
asked Nov 22 '18 at 0:48
LoliLoli
342310
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
edited Nov 22 '18 at 2:48
Chinnapparaj R
5,2481828
5,2481828
asked Nov 22 '18 at 0:48
LoliLoli
342310
asked Nov 22 '18 at 0:48
LoliLoli
342310
asked Nov 22 '18 at 0:48
LoliLoli
342310
342310
no one knows? :(
– Loli
Nov 22 '18 at 1:07
Try posting this on mathematica.se.
– rogerl
Nov 22 '18 at 2:27
add a comment |
no one knows? :(
– Loli
Nov 22 '18 at 1:07
Try posting this on mathematica.se.
– rogerl
Nov 22 '18 at 2:27
no one knows? :(
– Loli
Nov 22 '18 at 1:07
no one knows? :(
– Loli
Nov 22 '18 at 1:07
Try posting this on mathematica.se.
– rogerl
Nov 22 '18 at 2:27
Try posting this on mathematica.se.
– rogerl
Nov 22 '18 at 2:27
add a comment |
1 Answer
1
active
oldest
votes
Yes! Wolfram alpha is wrong. It says also the group $Bbb Z_3 times Bbb Z_2$ is not cyclic! , which is false.
The group $Bbb Z_{13} times Bbb Z_{12}$ is cyclic of order $156$ since $gcd{13,12}=1$ and $(5,1)$ is of order $ text{lcm}{13,12}=156$, so $$langle (5,1) rangle=Bbb Z_{13} times Bbb Z_{12}$$
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
Also see this link . It already says $Bbb{Z}_3 times Bbb{Z}_2$ is not cyclic but in this link, it list the six elements of this group as $1,a,a^2,a^3,a^4,a^5$. That is every element can be written as $a^n$ .which is exactly the cyclic group notation but nevertheless it says the group is not cyclic! which is false!
– Chinnapparaj R
Nov 22 '18 at 2:58
add a comment |
Your Answer
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Yes! Wolfram alpha is wrong. It says also the group $Bbb Z_3 times Bbb Z_2$ is not cyclic! , which is false.
The group $Bbb Z_{13} times Bbb Z_{12}$ is cyclic of order $156$ since $gcd{13,12}=1$ and $(5,1)$ is of order $ text{lcm}{13,12}=156$, so $$langle (5,1) rangle=Bbb Z_{13} times Bbb Z_{12}$$
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
Also see this link . It already says $Bbb{Z}_3 times Bbb{Z}_2$ is not cyclic but in this link, it list the six elements of this group as $1,a,a^2,a^3,a^4,a^5$. That is every element can be written as $a^n$ .which is exactly the cyclic group notation but nevertheless it says the group is not cyclic! which is false!
– Chinnapparaj R
Nov 22 '18 at 2:58
add a comment |
Yes! Wolfram alpha is wrong. It says also the group $Bbb Z_3 times Bbb Z_2$ is not cyclic! , which is false.
The group $Bbb Z_{13} times Bbb Z_{12}$ is cyclic of order $156$ since $gcd{13,12}=1$ and $(5,1)$ is of order $ text{lcm}{13,12}=156$, so $$langle (5,1) rangle=Bbb Z_{13} times Bbb Z_{12}$$
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
Also see this link . It already says $Bbb{Z}_3 times Bbb{Z}_2$ is not cyclic but in this link, it list the six elements of this group as $1,a,a^2,a^3,a^4,a^5$. That is every element can be written as $a^n$ .which is exactly the cyclic group notation but nevertheless it says the group is not cyclic! which is false!
– Chinnapparaj R
Nov 22 '18 at 2:58
add a comment |
Yes! Wolfram alpha is wrong. It says also the group $Bbb Z_3 times Bbb Z_2$ is not cyclic! , which is false.
The group $Bbb Z_{13} times Bbb Z_{12}$ is cyclic of order $156$ since $gcd{13,12}=1$ and $(5,1)$ is of order $ text{lcm}{13,12}=156$, so $$langle (5,1) rangle=Bbb Z_{13} times Bbb Z_{12}$$
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
Yes! Wolfram alpha is wrong. It says also the group $Bbb Z_3 times Bbb Z_2$ is not cyclic! , which is false.
The group $Bbb Z_{13} times Bbb Z_{12}$ is cyclic of order $156$ since $gcd{13,12}=1$ and $(5,1)$ is of order $ text{lcm}{13,12}=156$, so $$langle (5,1) rangle=Bbb Z_{13} times Bbb Z_{12}$$
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
answered Nov 22 '18 at 2:42
Chinnapparaj RChinnapparaj R
5,2481828
5,2481828
Also see this link . It already says $Bbb{Z}_3 times Bbb{Z}_2$ is not cyclic but in this link, it list the six elements of this group as $1,a,a^2,a^3,a^4,a^5$. That is every element can be written as $a^n$ .which is exactly the cyclic group notation but nevertheless it says the group is not cyclic! which is false!
– Chinnapparaj R
Nov 22 '18 at 2:58
add a comment |
Also see this link . It already says $Bbb{Z}_3 times Bbb{Z}_2$ is not cyclic but in this link, it list the six elements of this group as $1,a,a^2,a^3,a^4,a^5$. That is every element can be written as $a^n$ .which is exactly the cyclic group notation but nevertheless it says the group is not cyclic! which is false!
– Chinnapparaj R
Nov 22 '18 at 2:58
Also see this link . It already says $Bbb{Z}_3 times Bbb{Z}_2$ is not cyclic but in this link, it list the six elements of this group as $1,a,a^2,a^3,a^4,a^5$. That is every element can be written as $a^n$ .which is exactly the cyclic group notation but nevertheless it says the group is not cyclic! which is false!
– Chinnapparaj R
Nov 22 '18 at 2:58
Also see this link . It already says $Bbb{Z}_3 times Bbb{Z}_2$ is not cyclic but in this link, it list the six elements of this group as $1,a,a^2,a^3,a^4,a^5$. That is every element can be written as $a^n$ .which is exactly the cyclic group notation but nevertheless it says the group is not cyclic! which is false!
– Chinnapparaj R
Nov 22 '18 at 2:58
add a comment |
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no one knows? :(
– Loli
Nov 22 '18 at 1:07
Try posting this on mathematica.se.
– rogerl
Nov 22 '18 at 2:27