Find representative for each conjugacy class of $D_10$counting the number of elements in a conjugacy class of $S_n$The order of the representative elements of conjugacy classesSplitting of conjugacy class in $A_n$Conjugacy classes for rotations of $D_2n$Determining the conjugacy classes of a non-abelian group $G$ of order $8$Conjugacy class trivial proofLargest conjugacy class of $S_n$Number of conjugacy classes of a Dihedral group?Representatives for all conjugacy classes of elements of order 15 in A11How do I find the conjugacy classes of $A_4$?
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Find representative for each conjugacy class of $D_10$
counting the number of elements in a conjugacy class of $S_n$The order of the representative elements of conjugacy classesSplitting of conjugacy class in $A_n$Conjugacy classes for rotations of $D_2n$Determining the conjugacy classes of a non-abelian group $G$ of order $8$Conjugacy class trivial proofLargest conjugacy class of $S_n$Number of conjugacy classes of a Dihedral group?Representatives for all conjugacy classes of elements of order 15 in A11How do I find the conjugacy classes of $A_4$?
$begingroup$
How do you find representative for each conjugacy class of $D_10 = langle r rangle_5 rtimes langle s rangle_2$?
I know $D_10$ has $4$ conjugacy classes which are:
$[Id]$, $[r]$, $[r^2]$, $[s]$.
abstract-algebra group-theory finite-groups dihedral-groups
edited Mar 13 at 21:06
Yanior Weg
2,52911346
asked Mar 13 at 17:42
Sammy.dSammy.d
325
$endgroup$
add a comment |
$begingroup$
How do you find representative for each conjugacy class of $D_10 = langle r rangle_5 rtimes langle s rangle_2$?
I know $D_10$ has $4$ conjugacy classes which are:
$[Id]$, $[r]$, $[r^2]$, $[s]$.
abstract-algebra group-theory finite-groups dihedral-groups
edited Mar 13 at 21:06
Yanior Weg
2,52911346
asked Mar 13 at 17:42
Sammy.dSammy.d
325
$endgroup$
3
$begingroup$
Since conventions vary on this one - is your $D_10$ a group with ten elements, or a group with twenty elements?
$endgroup$
– jmerry
Mar 13 at 18:13
$begingroup$
With 10 elements @jmerry
$endgroup$
– Sammy.d
Mar 13 at 18:22
add a comment |
$begingroup$
How do you find representative for each conjugacy class of $D_10 = langle r rangle_5 rtimes langle s rangle_2$?
I know $D_10$ has $4$ conjugacy classes which are:
$[Id]$, $[r]$, $[r^2]$, $[s]$.
abstract-algebra group-theory finite-groups dihedral-groups
edited Mar 13 at 21:06
Yanior Weg
2,52911346
asked Mar 13 at 17:42
Sammy.dSammy.d
325
$endgroup$
How do you find representative for each conjugacy class of $D_10 = langle r rangle_5 rtimes langle s rangle_2$?
I know $D_10$ has $4$ conjugacy classes which are:
$[Id]$, $[r]$, $[r^2]$, $[s]$.
abstract-algebra group-theory finite-groups dihedral-groups
abstract-algebra group-theory finite-groups dihedral-groups
edited Mar 13 at 21:06
Yanior Weg
2,52911346
asked Mar 13 at 17:42
Sammy.dSammy.d
325
edited Mar 13 at 21:06
Yanior Weg
2,52911346
asked Mar 13 at 17:42
Sammy.dSammy.d
325
edited Mar 13 at 21:06
Yanior Weg
2,52911346
edited Mar 13 at 21:06
Yanior Weg
2,52911346
edited Mar 13 at 21:06
Yanior Weg
2,52911346
2,52911346
asked Mar 13 at 17:42
Sammy.dSammy.d
325
asked Mar 13 at 17:42
Sammy.dSammy.d
325
asked Mar 13 at 17:42
Sammy.dSammy.d
325
325
3
$begingroup$
Since conventions vary on this one - is your $D_10$ a group with ten elements, or a group with twenty elements?
$endgroup$
– jmerry
Mar 13 at 18:13
$begingroup$
With 10 elements @jmerry
$endgroup$
– Sammy.d
Mar 13 at 18:22
add a comment |
3
$begingroup$
Since conventions vary on this one - is your $D_10$ a group with ten elements, or a group with twenty elements?
$endgroup$
– jmerry
Mar 13 at 18:13
$begingroup$
With 10 elements @jmerry
$endgroup$
– Sammy.d
Mar 13 at 18:22
3
3
$begingroup$
Since conventions vary on this one - is your $D_10$ a group with ten elements, or a group with twenty elements?
$endgroup$
– jmerry
Mar 13 at 18:13
$begingroup$
Since conventions vary on this one - is your $D_10$ a group with ten elements, or a group with twenty elements?
$endgroup$
– jmerry
Mar 13 at 18:13
$begingroup$
With 10 elements @jmerry
$endgroup$
– Sammy.d
Mar 13 at 18:22
$begingroup$
With 10 elements @jmerry
$endgroup$
– Sammy.d
Mar 13 at 18:22
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Since you have already mentioned a representative for each conjugacy class in your question, I assume, that you want to know all representatives for each conjugacy class. Here they are:
$$[Id] = Id$$
$$[r] = r, r^4$$
$$[r^2] = r^2, r^3$$
$$[s] = s, rs, r^2s, r^3s, r^4s$$
More general information (concerning the solution of similar problem for $D_n$ with arbitrary $n$) can be found under this link:
https://groupprops.subwiki.org/wiki/Dihedral_group#Conjugacy_class_structure
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
$endgroup$
add a comment |
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$begingroup$
Since you have already mentioned a representative for each conjugacy class in your question, I assume, that you want to know all representatives for each conjugacy class. Here they are:
$$[Id] = Id$$
$$[r] = r, r^4$$
$$[r^2] = r^2, r^3$$
$$[s] = s, rs, r^2s, r^3s, r^4s$$
More general information (concerning the solution of similar problem for $D_n$ with arbitrary $n$) can be found under this link:
https://groupprops.subwiki.org/wiki/Dihedral_group#Conjugacy_class_structure
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
$endgroup$
add a comment |
$begingroup$
Since you have already mentioned a representative for each conjugacy class in your question, I assume, that you want to know all representatives for each conjugacy class. Here they are:
$$[Id] = Id$$
$$[r] = r, r^4$$
$$[r^2] = r^2, r^3$$
$$[s] = s, rs, r^2s, r^3s, r^4s$$
More general information (concerning the solution of similar problem for $D_n$ with arbitrary $n$) can be found under this link:
https://groupprops.subwiki.org/wiki/Dihedral_group#Conjugacy_class_structure
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
$endgroup$
add a comment |
$begingroup$
Since you have already mentioned a representative for each conjugacy class in your question, I assume, that you want to know all representatives for each conjugacy class. Here they are:
$$[Id] = Id$$
$$[r] = r, r^4$$
$$[r^2] = r^2, r^3$$
$$[s] = s, rs, r^2s, r^3s, r^4s$$
More general information (concerning the solution of similar problem for $D_n$ with arbitrary $n$) can be found under this link:
https://groupprops.subwiki.org/wiki/Dihedral_group#Conjugacy_class_structure
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
$endgroup$
Since you have already mentioned a representative for each conjugacy class in your question, I assume, that you want to know all representatives for each conjugacy class. Here they are:
$$[Id] = Id$$
$$[r] = r, r^4$$
$$[r^2] = r^2, r^3$$
$$[s] = s, rs, r^2s, r^3s, r^4s$$
More general information (concerning the solution of similar problem for $D_n$ with arbitrary $n$) can be found under this link:
https://groupprops.subwiki.org/wiki/Dihedral_group#Conjugacy_class_structure
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
answered Mar 13 at 21:06
Yanior WegYanior Weg
2,52911346
2,52911346
add a comment |
add a comment |
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3
$begingroup$
Since conventions vary on this one - is your $D_10$ a group with ten elements, or a group with twenty elements?
$endgroup$
– jmerry
Mar 13 at 18:13
$begingroup$
With 10 elements @jmerry
$endgroup$
– Sammy.d
Mar 13 at 18:22