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If H is a group, prove there exists elements such that.. [closed]

Prove that for every odd integer n, there is a group…prove of disprove :'For every $xin G$ there exists some $yin G$ such that $x=y^2$, where $G$ is a group."Prove or disprove: There exists a group $G$ and a normal subgroup $N$ such that $G$ is non-abelian, but both $N$ and $G/N$ are abelian.Prove that there exists subgroup of any order of any power of $p$ in a $p$-groupShow that there exists a positive integer $k$ such that $g^k=1_G$Prove that the group of order 3 is cyclic.Does there exists a finite abelian group $G$ containing exactly $60$ elements of order $2$?How do I show that there exists only one group of order 2 up to isomorphism?Does every non-elementary subgroup of the additive group of rationals contain prime multiples of elements in its complement?Group theory problem - the order of elements

-4

$begingroup$

If H is a group and given any elements $a,b in H$, prove there exists elements $x,y in H$ such that $ax=b$ and $a=by$.

Any help would be appreciated thank you.

abstract-algebra group-theory

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asked Mar 13 at 10:45

MathsRookieMathsRookie

987

$endgroup$

closed as off-topic by José Carlos Santos, user1729, Martin R, RRL, Shaun Mar 13 at 17:55

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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, user1729, Martin R, RRL, Shaun

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How would you do this for $H$ being the group of invertible $2times 2$-matrices?
  $endgroup$
  – Dietrich Burde
  Mar 13 at 10:52
  

  
  
  
  

add a comment | 

-4

$begingroup$

If H is a group and given any elements $a,b in H$, prove there exists elements $x,y in H$ such that $ax=b$ and $a=by$.

Any help would be appreciated thank you.

abstract-algebra group-theory

share|cite|improve this question

asked Mar 13 at 10:45

MathsRookieMathsRookie

987

$endgroup$

closed as off-topic by José Carlos Santos, user1729, Martin R, RRL, Shaun Mar 13 at 17:55

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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, user1729, Martin R, RRL, Shaun

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How would you do this for $H$ being the group of invertible $2times 2$-matrices?
  $endgroup$
  – Dietrich Burde
  Mar 13 at 10:52
  

  
  
  
  

add a comment | 

$begingroup$

If H is a group and given any elements $a,b in H$, prove there exists elements $x,y in H$ such that $ax=b$ and $a=by$.

Any help would be appreciated thank you.

abstract-algebra group-theory

share|cite|improve this question

asked Mar 13 at 10:45

MathsRookieMathsRookie

987

$endgroup$

share|cite|improve this question

asked Mar 13 at 10:45

MathsRookieMathsRookie

987

share|cite|improve this question

asked Mar 13 at 10:45

MathsRookieMathsRookie

987

asked Mar 13 at 10:45

MathsRookieMathsRookie

987

asked Mar 13 at 10:45

MathsRookieMathsRookie

987

1 Answer
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0

$begingroup$

Set $x = a^-1 b$ and $y = b^-1 a$.

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answered Mar 13 at 10:47

KezerKezer

1,458621

$endgroup$

add a comment | 

0

$begingroup$

Set $x = a^-1 b$ and $y = b^-1 a$.

share|cite|improve this answer

answered Mar 13 at 10:47

KezerKezer

1,458621

$endgroup$

add a comment | 

0

$begingroup$

Set $x = a^-1 b$ and $y = b^-1 a$.

share|cite|improve this answer

answered Mar 13 at 10:47

KezerKezer

1,458621

$endgroup$

add a comment | 

$begingroup$

Set $x = a^-1 b$ and $y = b^-1 a$.

share|cite|improve this answer

answered Mar 13 at 10:47

KezerKezer

1,458621

$endgroup$

share|cite|improve this answer

answered Mar 13 at 10:47

KezerKezer

1,458621

answered Mar 13 at 10:47

KezerKezer

1,458621

answered Mar 13 at 10:47

KezerKezer

1,458621