Finite Engel group is nilpotent.
3
$begingroup$
A group $G$ is said to be $n$ engel if
$$[x,[x, dots ,[x,y]]dots ]=1,$$
where $x$ appears $n$ times, and this holds for all $x,yin G$.
We know there is infinite order engel group which is not nilpotent.
But what can we say about finite order engel groups, are they always nilpotent?
abstract-algebra group-theory finite-groups nilpotent-groups
edited Jan 3 at 10:02
Shaun
9,933113684
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
$endgroup$
|
show 3 more comments
3
$begingroup$
A group $G$ is said to be $n$ engel if
$$[x,[x, dots ,[x,y]]dots ]=1,$$
where $x$ appears $n$ times, and this holds for all $x,yin G$.
We know there is infinite order engel group which is not nilpotent.
But what can we say about finite order engel groups, are they always nilpotent?
abstract-algebra group-theory finite-groups nilpotent-groups
edited Jan 3 at 10:02
Shaun
9,933113684
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
$endgroup$
$begingroup$
You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
$endgroup$
– Shaun
Jan 3 at 9:55
$begingroup$
Actually, I was studying about the Engel groups and this question arises that weather finite $n$ Engel groups are nilpotent or not.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:00
1
$begingroup$
The answer is YES (Zorn, 1936), see groupsstandrews.org/2009/Talks/Traustason.pdf
$endgroup$
– Nicky Hekster
Jan 3 at 10:09
$begingroup$
#Nicky Hekster thanks for the reply, $groupsstandrews.org/2009/Talks/Traustason.pdf$ here only statement is given please tell me that how to prove this result.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:14
2
$begingroup$
This looks like a reasonable request about the state of knowledge concerning a research topic rather than a "here is my problem solve it for me" question, so I would not vote for closing it for lack of context.
$endgroup$
– Derek Holt
Jan 3 at 11:40
|
show 3 more comments
3
3
3
2
$begingroup$
A group $G$ is said to be $n$ engel if
$$[x,[x, dots ,[x,y]]dots ]=1,$$
where $x$ appears $n$ times, and this holds for all $x,yin G$.
We know there is infinite order engel group which is not nilpotent.
But what can we say about finite order engel groups, are they always nilpotent?
abstract-algebra group-theory finite-groups nilpotent-groups
edited Jan 3 at 10:02
Shaun
9,933113684
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
$endgroup$
A group $G$ is said to be $n$ engel if
$$[x,[x, dots ,[x,y]]dots ]=1,$$
where $x$ appears $n$ times, and this holds for all $x,yin G$.
We know there is infinite order engel group which is not nilpotent.
But what can we say about finite order engel groups, are they always nilpotent?
abstract-algebra group-theory finite-groups nilpotent-groups
abstract-algebra group-theory finite-groups nilpotent-groups
edited Jan 3 at 10:02
Shaun
9,933113684
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
edited Jan 3 at 10:02
Shaun
9,933113684
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
edited Jan 3 at 10:02
Shaun
9,933113684
edited Jan 3 at 10:02
Shaun
9,933113684
edited Jan 3 at 10:02
Shaun
9,933113684
9,933113684
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
asked Jan 3 at 9:47
MANI SHANKAR PANDEYMANI SHANKAR PANDEY
548
548
$begingroup$
You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
$endgroup$
– Shaun
Jan 3 at 9:55
$begingroup$
Actually, I was studying about the Engel groups and this question arises that weather finite $n$ Engel groups are nilpotent or not.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:00
1
$begingroup$
The answer is YES (Zorn, 1936), see groupsstandrews.org/2009/Talks/Traustason.pdf
$endgroup$
– Nicky Hekster
Jan 3 at 10:09
$begingroup$
#Nicky Hekster thanks for the reply, $groupsstandrews.org/2009/Talks/Traustason.pdf$ here only statement is given please tell me that how to prove this result.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:14
2
$begingroup$
This looks like a reasonable request about the state of knowledge concerning a research topic rather than a "here is my problem solve it for me" question, so I would not vote for closing it for lack of context.
$endgroup$
– Derek Holt
Jan 3 at 11:40
|
show 3 more comments
$begingroup$
You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
$endgroup$
– Shaun
Jan 3 at 9:55
$begingroup$
Actually, I was studying about the Engel groups and this question arises that weather finite $n$ Engel groups are nilpotent or not.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:00
1
$begingroup$
The answer is YES (Zorn, 1936), see groupsstandrews.org/2009/Talks/Traustason.pdf
$endgroup$
– Nicky Hekster
Jan 3 at 10:09
$begingroup$
#Nicky Hekster thanks for the reply, $groupsstandrews.org/2009/Talks/Traustason.pdf$ here only statement is given please tell me that how to prove this result.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:14
2
$begingroup$
This looks like a reasonable request about the state of knowledge concerning a research topic rather than a "here is my problem solve it for me" question, so I would not vote for closing it for lack of context.
$endgroup$
– Derek Holt
Jan 3 at 11:40
$begingroup$
You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
$endgroup$
– Shaun
Jan 3 at 9:55
$begingroup$
You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
$endgroup$
– Shaun
Jan 3 at 9:55
$begingroup$
Actually, I was studying about the Engel groups and this question arises that weather finite $n$ Engel groups are nilpotent or not.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:00
$begingroup$
Actually, I was studying about the Engel groups and this question arises that weather finite $n$ Engel groups are nilpotent or not.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:00
1
1
$begingroup$
The answer is YES (Zorn, 1936), see groupsstandrews.org/2009/Talks/Traustason.pdf
$endgroup$
– Nicky Hekster
Jan 3 at 10:09
$begingroup$
The answer is YES (Zorn, 1936), see groupsstandrews.org/2009/Talks/Traustason.pdf
$endgroup$
– Nicky Hekster
Jan 3 at 10:09
$begingroup$
#Nicky Hekster thanks for the reply, $groupsstandrews.org/2009/Talks/Traustason.pdf$ here only statement is given please tell me that how to prove this result.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:14
$begingroup$
#Nicky Hekster thanks for the reply, $groupsstandrews.org/2009/Talks/Traustason.pdf$ here only statement is given please tell me that how to prove this result.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:14
2
2
$begingroup$
This looks like a reasonable request about the state of knowledge concerning a research topic rather than a "here is my problem solve it for me" question, so I would not vote for closing it for lack of context.
$endgroup$
– Derek Holt
Jan 3 at 11:40
$begingroup$
This looks like a reasonable request about the state of knowledge concerning a research topic rather than a "here is my problem solve it for me" question, so I would not vote for closing it for lack of context.
$endgroup$
– Derek Holt
Jan 3 at 11:40
|
show 3 more comments
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$begingroup$
You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
$endgroup$
– Shaun
Jan 3 at 9:55
$begingroup$
Actually, I was studying about the Engel groups and this question arises that weather finite $n$ Engel groups are nilpotent or not.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:00
1
$begingroup$
The answer is YES (Zorn, 1936), see groupsstandrews.org/2009/Talks/Traustason.pdf
$endgroup$
– Nicky Hekster
Jan 3 at 10:09
$begingroup$
#Nicky Hekster thanks for the reply, $groupsstandrews.org/2009/Talks/Traustason.pdf$ here only statement is given please tell me that how to prove this result.
$endgroup$
– MANI SHANKAR PANDEY
Jan 3 at 10:14
2
$begingroup$
This looks like a reasonable request about the state of knowledge concerning a research topic rather than a "here is my problem solve it for me" question, so I would not vote for closing it for lack of context.
$endgroup$
– Derek Holt
Jan 3 at 11:40