Mixing
When does $C(a^i)=C(a^j)$ if $|a|$ is finite?
1
$begingroup$
I am looking for a necessary and sufficient condition for $C(a^i)=C(a^j)$ to hold in a general group G given that $|a|$ is finite and known.
What if $|a|$ is a prime?
Here $C(a)={gin G ;| ;gag^{-1}=a}$
group-theory
asked Jan 23 at 16:00
AbhayAbhay
3789
$endgroup$
add a comment |
1
$begingroup$
I am looking for a necessary and sufficient condition for $C(a^i)=C(a^j)$ to hold in a general group G given that $|a|$ is finite and known.
What if $|a|$ is a prime?
Here $C(a)={gin G ;| ;gag^{-1}=a}$
group-theory
asked Jan 23 at 16:00
AbhayAbhay
3789
$endgroup$
$begingroup$
Do you want it to hold for all $i,j$ or are you asking for a condition depending on $i,j$ that would imply $C(a^i)=C(a^j)$ for that particular $i,j$?
$endgroup$
– Levent
Jan 24 at 1:09
$begingroup$
@Levent Yes, I am
$endgroup$
– Abhay
Jan 25 at 1:53
$begingroup$
I don't think you are answering my question. Do you want it to hold for all $i,j$?
$endgroup$
– Levent
Jan 25 at 13:49
add a comment |
1
1
1
1
$begingroup$
I am looking for a necessary and sufficient condition for $C(a^i)=C(a^j)$ to hold in a general group G given that $|a|$ is finite and known.
What if $|a|$ is a prime?
Here $C(a)={gin G ;| ;gag^{-1}=a}$
group-theory
asked Jan 23 at 16:00
AbhayAbhay
3789
$endgroup$
I am looking for a necessary and sufficient condition for $C(a^i)=C(a^j)$ to hold in a general group G given that $|a|$ is finite and known.
What if $|a|$ is a prime?
Here $C(a)={gin G ;| ;gag^{-1}=a}$
group-theory
group-theory
asked Jan 23 at 16:00
AbhayAbhay
3789
asked Jan 23 at 16:00
AbhayAbhay
3789
asked Jan 23 at 16:00
AbhayAbhay
3789
asked Jan 23 at 16:00
AbhayAbhay
3789
asked Jan 23 at 16:00
AbhayAbhay
3789
3789
$begingroup$
Do you want it to hold for all $i,j$ or are you asking for a condition depending on $i,j$ that would imply $C(a^i)=C(a^j)$ for that particular $i,j$?
$endgroup$
– Levent
Jan 24 at 1:09
$begingroup$
@Levent Yes, I am
$endgroup$
– Abhay
Jan 25 at 1:53
$begingroup$
I don't think you are answering my question. Do you want it to hold for all $i,j$?
$endgroup$
– Levent
Jan 25 at 13:49
add a comment |
$begingroup$
Do you want it to hold for all $i,j$ or are you asking for a condition depending on $i,j$ that would imply $C(a^i)=C(a^j)$ for that particular $i,j$?
$endgroup$
– Levent
Jan 24 at 1:09
$begingroup$
@Levent Yes, I am
$endgroup$
– Abhay
Jan 25 at 1:53
$begingroup$
I don't think you are answering my question. Do you want it to hold for all $i,j$?
$endgroup$
– Levent
Jan 25 at 13:49
$begingroup$
Do you want it to hold for all $i,j$ or are you asking for a condition depending on $i,j$ that would imply $C(a^i)=C(a^j)$ for that particular $i,j$?
$endgroup$
– Levent
Jan 24 at 1:09
$begingroup$
Do you want it to hold for all $i,j$ or are you asking for a condition depending on $i,j$ that would imply $C(a^i)=C(a^j)$ for that particular $i,j$?
$endgroup$
– Levent
Jan 24 at 1:09
$begingroup$
@Levent Yes, I am
$endgroup$
– Abhay
Jan 25 at 1:53
$begingroup$
@Levent Yes, I am
$endgroup$
– Abhay
Jan 25 at 1:53
$begingroup$
I don't think you are answering my question. Do you want it to hold for all $i,j$?
$endgroup$
– Levent
Jan 25 at 13:49
$begingroup$
I don't think you are answering my question. Do you want it to hold for all $i,j$?
$endgroup$
– Levent
Jan 25 at 13:49
add a comment |
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$begingroup$
Do you want it to hold for all $i,j$ or are you asking for a condition depending on $i,j$ that would imply $C(a^i)=C(a^j)$ for that particular $i,j$?
$endgroup$
– Levent
Jan 24 at 1:09
$begingroup$
@Levent Yes, I am
$endgroup$
– Abhay
Jan 25 at 1:53
$begingroup$
I don't think you are answering my question. Do you want it to hold for all $i,j$?
$endgroup$
– Levent
Jan 25 at 13:49