What is meant by determine $(Gtimes G)/D$?
$begingroup$
Let $G$ be a group and $D:={(g,g) in G times G: g in G}$
Determine: $(G times G)/D$
I do not even know what is being asked for here. Any ideas?
Must I determine a particular map with the homomorphism theorem?
linear-algebra abstract-algebra group-theory
$endgroup$
add a comment |
$begingroup$
Let $G$ be a group and $D:={(g,g) in G times G: g in G}$
Determine: $(G times G)/D$
I do not even know what is being asked for here. Any ideas?
Must I determine a particular map with the homomorphism theorem?
linear-algebra abstract-algebra group-theory
$endgroup$
1
$begingroup$
You mean of course $(G times G)/D$, and since if $G$ is non-commutative $D$ is not a normal subgroup of $G times G$, it is probably intended for you to find representatives of the cosets of $D$ in $G times G$.
$endgroup$
– Andreas Caranti
Jan 14 at 10:12
4
$begingroup$
I agree that it is very unclear what is being asked for here.
$endgroup$
– Derek Holt
Jan 14 at 10:24
$begingroup$
Or to find an isomorphism of the $(Gtimes G)$-set of cosets of $D$ with a more familiar $(Gtimes G)$-set.
$endgroup$
– C Monsour
Jan 14 at 14:22
add a comment |
$begingroup$
Let $G$ be a group and $D:={(g,g) in G times G: g in G}$
Determine: $(G times G)/D$
I do not even know what is being asked for here. Any ideas?
Must I determine a particular map with the homomorphism theorem?
linear-algebra abstract-algebra group-theory
$endgroup$
Let $G$ be a group and $D:={(g,g) in G times G: g in G}$
Determine: $(G times G)/D$
I do not even know what is being asked for here. Any ideas?
Must I determine a particular map with the homomorphism theorem?
linear-algebra abstract-algebra group-theory
linear-algebra abstract-algebra group-theory
edited Jan 14 at 10:23
MinaThuma
asked Jan 14 at 9:58
MinaThumaMinaThuma
1558
1558
1
$begingroup$
You mean of course $(G times G)/D$, and since if $G$ is non-commutative $D$ is not a normal subgroup of $G times G$, it is probably intended for you to find representatives of the cosets of $D$ in $G times G$.
$endgroup$
– Andreas Caranti
Jan 14 at 10:12
4
$begingroup$
I agree that it is very unclear what is being asked for here.
$endgroup$
– Derek Holt
Jan 14 at 10:24
$begingroup$
Or to find an isomorphism of the $(Gtimes G)$-set of cosets of $D$ with a more familiar $(Gtimes G)$-set.
$endgroup$
– C Monsour
Jan 14 at 14:22
add a comment |
1
$begingroup$
You mean of course $(G times G)/D$, and since if $G$ is non-commutative $D$ is not a normal subgroup of $G times G$, it is probably intended for you to find representatives of the cosets of $D$ in $G times G$.
$endgroup$
– Andreas Caranti
Jan 14 at 10:12
4
$begingroup$
I agree that it is very unclear what is being asked for here.
$endgroup$
– Derek Holt
Jan 14 at 10:24
$begingroup$
Or to find an isomorphism of the $(Gtimes G)$-set of cosets of $D$ with a more familiar $(Gtimes G)$-set.
$endgroup$
– C Monsour
Jan 14 at 14:22
1
1
$begingroup$
You mean of course $(G times G)/D$, and since if $G$ is non-commutative $D$ is not a normal subgroup of $G times G$, it is probably intended for you to find representatives of the cosets of $D$ in $G times G$.
$endgroup$
– Andreas Caranti
Jan 14 at 10:12
$begingroup$
You mean of course $(G times G)/D$, and since if $G$ is non-commutative $D$ is not a normal subgroup of $G times G$, it is probably intended for you to find representatives of the cosets of $D$ in $G times G$.
$endgroup$
– Andreas Caranti
Jan 14 at 10:12
4
4
$begingroup$
I agree that it is very unclear what is being asked for here.
$endgroup$
– Derek Holt
Jan 14 at 10:24
$begingroup$
I agree that it is very unclear what is being asked for here.
$endgroup$
– Derek Holt
Jan 14 at 10:24
$begingroup$
Or to find an isomorphism of the $(Gtimes G)$-set of cosets of $D$ with a more familiar $(Gtimes G)$-set.
$endgroup$
– C Monsour
Jan 14 at 14:22
$begingroup$
Or to find an isomorphism of the $(Gtimes G)$-set of cosets of $D$ with a more familiar $(Gtimes G)$-set.
$endgroup$
– C Monsour
Jan 14 at 14:22
add a comment |
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1
$begingroup$
You mean of course $(G times G)/D$, and since if $G$ is non-commutative $D$ is not a normal subgroup of $G times G$, it is probably intended for you to find representatives of the cosets of $D$ in $G times G$.
$endgroup$
– Andreas Caranti
Jan 14 at 10:12
4
$begingroup$
I agree that it is very unclear what is being asked for here.
$endgroup$
– Derek Holt
Jan 14 at 10:24
$begingroup$
Or to find an isomorphism of the $(Gtimes G)$-set of cosets of $D$ with a more familiar $(Gtimes G)$-set.
$endgroup$
– C Monsour
Jan 14 at 14:22