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

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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













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$begingroup$



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.










share|cite|improve this question









$endgroup$



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















-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.










share|cite|improve this question









$endgroup$



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













-4












-4








-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.










share|cite|improve this question









$endgroup$





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













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 13 at 10:45









MathsRookieMathsRookie

987




987




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.







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
















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















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




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










1 Answer
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$begingroup$

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






share|cite|improve this answer









$endgroup$



















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0












    $begingroup$

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






    share|cite|improve this answer









    $endgroup$

















      0












      $begingroup$

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






      share|cite|improve this answer









      $endgroup$















        0












        0








        0





        $begingroup$

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






        share|cite|improve this answer









        $endgroup$



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







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Mar 13 at 10:47









        KezerKezer

        1,458621




        1,458621













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