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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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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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
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
$endgroup$
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
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How would you do this for $H$ being the group of invertible $2times 2$-matrices?
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– 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
$endgroup$
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
abstract-algebra group-theory
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
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
$begingroup$
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 |
$begingroup$
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
add a comment |
1 Answer
1
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$begingroup$
Set $x = a^-1 b$ and $y = b^-1 a$.
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Set $x = a^-1 b$ and $y = b^-1 a$.
$endgroup$
add a comment |
$begingroup$
Set $x = a^-1 b$ and $y = b^-1 a$.
$endgroup$
add a comment |
$begingroup$
Set $x = a^-1 b$ and $y = b^-1 a$.
$endgroup$
Set $x = a^-1 b$ and $y = b^-1 a$.
answered Mar 13 at 10:47
KezerKezer
1,458621
1,458621
add a comment |
add a comment |
$begingroup$
How would you do this for $H$ being the group of invertible $2times 2$-matrices?
$endgroup$
– Dietrich Burde
Mar 13 at 10:52