Problem on cyclic subgroup [on hold]
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Show that if $G$ is a group that contains cyclic subgroups of order $4,5$ then there must exist an element of order $20$ in $ G$.
I don't know how to prove it. I'm just beginner.Thanks for help .
abstract-algebra group-theory
edited 2 days ago
Chinnapparaj R
4,6081725
asked 2 days ago
G C R
164
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G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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put on hold as off-topic by Derek Holt, Gibbs, Christopher, amWhy, Rebellos 2 days ago
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." – Derek Holt, Gibbs, Christopher, amWhy, Rebellos
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
favorite
Show that if $G$ is a group that contains cyclic subgroups of order $4,5$ then there must exist an element of order $20$ in $ G$.
I don't know how to prove it. I'm just beginner.Thanks for help .
abstract-algebra group-theory
edited 2 days ago
Chinnapparaj R
4,6081725
asked 2 days ago
G C R
164
New contributor
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Derek Holt, Gibbs, Christopher, amWhy, Rebellos 2 days ago
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." – Derek Holt, Gibbs, Christopher, amWhy, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Why are you asking us to show something that is false? Where did this problem come from?
– Derek Holt
2 days ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Show that if $G$ is a group that contains cyclic subgroups of order $4,5$ then there must exist an element of order $20$ in $ G$.
I don't know how to prove it. I'm just beginner.Thanks for help .
abstract-algebra group-theory
edited 2 days ago
Chinnapparaj R
4,6081725
asked 2 days ago
G C R
164
New contributor
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Show that if $G$ is a group that contains cyclic subgroups of order $4,5$ then there must exist an element of order $20$ in $ G$.
I don't know how to prove it. I'm just beginner.Thanks for help .
abstract-algebra group-theory
abstract-algebra group-theory
edited 2 days ago
Chinnapparaj R
4,6081725
asked 2 days ago
G C R
164
New contributor
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Chinnapparaj R
4,6081725
asked 2 days ago
G C R
164
New contributor
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Chinnapparaj R
4,6081725
edited 2 days ago
Chinnapparaj R
4,6081725
edited 2 days ago
Chinnapparaj R
4,6081725
4,6081725
asked 2 days ago
G C R
164
New contributor
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
G C R
164
asked 2 days ago
G C R
164
164
New contributor
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
G C R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Derek Holt, Gibbs, Christopher, amWhy, Rebellos 2 days ago
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." – Derek Holt, Gibbs, Christopher, amWhy, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Derek Holt, Gibbs, Christopher, amWhy, Rebellos 2 days ago
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." – Derek Holt, Gibbs, Christopher, amWhy, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Why are you asking us to show something that is false? Where did this problem come from?
– Derek Holt
2 days ago
add a comment |
1
Why are you asking us to show something that is false? Where did this problem come from?
– Derek Holt
2 days ago
1
1
Why are you asking us to show something that is false? Where did this problem come from?
– Derek Holt
2 days ago
Why are you asking us to show something that is false? Where did this problem come from?
– Derek Holt
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
up vote
6
down vote
accepted
It is false, in general! For example, if we take $G=S_5$, then $G$ has cyclic subgroups of order $4$ and $5$,but $G$ has no element of order $20$.
If $G$ is Abelian then this result is true! Call $H$ the cyclic subgroup of order $4$ and $K$,the cyclic subgroups of order $5$ in $G$. So $exists a in H wedge b in K$ so that $vert a vert=4$ and $vert b vert=5$.
Now, all we know is about only $a$ and $b$, so use these two to produce the another element of order $20$.
Here $ab=ba$ implies $ab$ is the required element of order $20$.
answered 2 days ago
Chinnapparaj R
4,6081725
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
accepted
It is false, in general! For example, if we take $G=S_5$, then $G$ has cyclic subgroups of order $4$ and $5$,but $G$ has no element of order $20$.
If $G$ is Abelian then this result is true! Call $H$ the cyclic subgroup of order $4$ and $K$,the cyclic subgroups of order $5$ in $G$. So $exists a in H wedge b in K$ so that $vert a vert=4$ and $vert b vert=5$.
Now, all we know is about only $a$ and $b$, so use these two to produce the another element of order $20$.
Here $ab=ba$ implies $ab$ is the required element of order $20$.
answered 2 days ago
Chinnapparaj R
4,6081725
add a comment |
up vote
6
down vote
accepted
It is false, in general! For example, if we take $G=S_5$, then $G$ has cyclic subgroups of order $4$ and $5$,but $G$ has no element of order $20$.
If $G$ is Abelian then this result is true! Call $H$ the cyclic subgroup of order $4$ and $K$,the cyclic subgroups of order $5$ in $G$. So $exists a in H wedge b in K$ so that $vert a vert=4$ and $vert b vert=5$.
Now, all we know is about only $a$ and $b$, so use these two to produce the another element of order $20$.
Here $ab=ba$ implies $ab$ is the required element of order $20$.
answered 2 days ago
Chinnapparaj R
4,6081725
add a comment |
up vote
6
down vote
accepted
up vote
6
down vote
accepted
It is false, in general! For example, if we take $G=S_5$, then $G$ has cyclic subgroups of order $4$ and $5$,but $G$ has no element of order $20$.
If $G$ is Abelian then this result is true! Call $H$ the cyclic subgroup of order $4$ and $K$,the cyclic subgroups of order $5$ in $G$. So $exists a in H wedge b in K$ so that $vert a vert=4$ and $vert b vert=5$.
Now, all we know is about only $a$ and $b$, so use these two to produce the another element of order $20$.
Here $ab=ba$ implies $ab$ is the required element of order $20$.
answered 2 days ago
Chinnapparaj R
4,6081725
It is false, in general! For example, if we take $G=S_5$, then $G$ has cyclic subgroups of order $4$ and $5$,but $G$ has no element of order $20$.
If $G$ is Abelian then this result is true! Call $H$ the cyclic subgroup of order $4$ and $K$,the cyclic subgroups of order $5$ in $G$. So $exists a in H wedge b in K$ so that $vert a vert=4$ and $vert b vert=5$.
Now, all we know is about only $a$ and $b$, so use these two to produce the another element of order $20$.
Here $ab=ba$ implies $ab$ is the required element of order $20$.
answered 2 days ago
Chinnapparaj R
4,6081725
answered 2 days ago
Chinnapparaj R
4,6081725
answered 2 days ago
Chinnapparaj R
4,6081725
answered 2 days ago
Chinnapparaj R
4,6081725
4,6081725
add a comment |
add a comment |
1
Why are you asking us to show something that is false? Where did this problem come from?
– Derek Holt
2 days ago