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If there is an $x_0$ of order two and $operatorname{ord}f(x_0)^{k}=2$, $k={0,…,p-1}$, then $x^2=e$.

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0

$begingroup$

I have a group $G={e,f(x),dots ,f(x)^{p-1}}$ and $fin operatorname{Aut}(G)$ and as $|G|$ is even, I read the following property:

If there is an $x_0$ of order two and $ operatorname{ord}f(x_0)^{k}=2$, $k=0,dots ,p-1$, then $x^2=e$ for any $x in G$.

I am not sure I understand it as I should.

abstract-algebra group-theory finite-groups

share|cite|improve this question

edited Mar 13 at 22:00

Shaun

9,690113684

asked Mar 13 at 8:41

user651754

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What do you know about generators?
  $endgroup$
  – Shaun
  Mar 13 at 22:01
  

  
  
  
  

add a comment | 

0

$begingroup$

I have a group $G={e,f(x),dots ,f(x)^{p-1}}$ and $fin operatorname{Aut}(G)$ and as $|G|$ is even, I read the following property:

If there is an $x_0$ of order two and $ operatorname{ord}f(x_0)^{k}=2$, $k=0,dots ,p-1$, then $x^2=e$ for any $x in G$.

I am not sure I understand it as I should.

abstract-algebra group-theory finite-groups

share|cite|improve this question

edited Mar 13 at 22:00

Shaun

9,690113684

asked Mar 13 at 8:41

user651754

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What do you know about generators?
  $endgroup$
  – Shaun
  Mar 13 at 22:01
  

  
  
  
  

add a comment | 

$begingroup$

I have a group $G={e,f(x),dots ,f(x)^{p-1}}$ and $fin operatorname{Aut}(G)$ and as $|G|$ is even, I read the following property:

If there is an $x_0$ of order two and $ operatorname{ord}f(x_0)^{k}=2$, $k=0,dots ,p-1$, then $x^2=e$ for any $x in G$.

I am not sure I understand it as I should.

abstract-algebra group-theory finite-groups

share|cite|improve this question

edited Mar 13 at 22:00

Shaun

9,690113684

asked Mar 13 at 8:41

user651754

$endgroup$

share|cite|improve this question

edited Mar 13 at 22:00

Shaun

9,690113684

asked Mar 13 at 8:41

user651754

share|cite|improve this question

edited Mar 13 at 22:00

Shaun

9,690113684

asked Mar 13 at 8:41

user651754

edited Mar 13 at 22:00

Shaun

9,690113684

edited Mar 13 at 22:00

Shaun

9,690113684