Mixing
What are the conjugacy classes in $A_5$?
$begingroup$
I'm new to group-theory and to the Alternating groups. In my book I got asked the following questions:
What are the conjugacy classes in $A_5$?
Where should I start? What does it mean, "conjugacy"?
group-theory definition symmetric-groups
edited Jan 1 at 18:59
Shaun
8,818113681
asked Jan 1 at 18:43
BadukBaduk
171
$endgroup$
|
show 1 more comment
$begingroup$
I'm new to group-theory and to the Alternating groups. In my book I got asked the following questions:
What are the conjugacy classes in $A_5$?
Where should I start? What does it mean, "conjugacy"?
group-theory definition symmetric-groups
edited Jan 1 at 18:59
Shaun
8,818113681
asked Jan 1 at 18:43
BadukBaduk
171
$endgroup$
1
$begingroup$
Which book are you using? Please edit the question to include the details.
$endgroup$
– Shaun
Jan 1 at 18:44
$begingroup$
For any $sigmain A_5$, the conjugacy map $c_sigma:A_5to A_5$ is defined by $c_sigma(tau)=sigma^{-1}tausigma$ for each $tauin A_5$.
$endgroup$
– Shaun
Jan 1 at 18:47
1
$begingroup$
en.wikipedia.org/wiki/Conjugacy_class
$endgroup$
– Lord Shark the Unknown
Jan 1 at 18:52
3
$begingroup$
I think you probably need to do some work on basic group theory concepts before trying to apply them.
$endgroup$
– Mark Bennet
Jan 1 at 19:04
1
$begingroup$
Start by looking up the word "conjugacy" in the text. How were you planning on solving the problem if you don't know what it means?
$endgroup$
– anomaly
Jan 1 at 20:38
|
show 1 more comment
$begingroup$
I'm new to group-theory and to the Alternating groups. In my book I got asked the following questions:
What are the conjugacy classes in $A_5$?
Where should I start? What does it mean, "conjugacy"?
group-theory definition symmetric-groups
edited Jan 1 at 18:59
Shaun
8,818113681
asked Jan 1 at 18:43
BadukBaduk
171
$endgroup$
I'm new to group-theory and to the Alternating groups. In my book I got asked the following questions:
What are the conjugacy classes in $A_5$?
Where should I start? What does it mean, "conjugacy"?
group-theory definition symmetric-groups
group-theory definition symmetric-groups
edited Jan 1 at 18:59
Shaun
8,818113681
asked Jan 1 at 18:43
BadukBaduk
171
edited Jan 1 at 18:59
Shaun
8,818113681
asked Jan 1 at 18:43
BadukBaduk
171
edited Jan 1 at 18:59
Shaun
8,818113681
edited Jan 1 at 18:59
Shaun
8,818113681
edited Jan 1 at 18:59
Shaun
8,818113681
8,818113681
asked Jan 1 at 18:43
BadukBaduk
171
asked Jan 1 at 18:43
BadukBaduk
171
asked Jan 1 at 18:43
BadukBaduk
171
171
1
$begingroup$
Which book are you using? Please edit the question to include the details.
$endgroup$
– Shaun
Jan 1 at 18:44
$begingroup$
For any $sigmain A_5$, the conjugacy map $c_sigma:A_5to A_5$ is defined by $c_sigma(tau)=sigma^{-1}tausigma$ for each $tauin A_5$.
$endgroup$
– Shaun
Jan 1 at 18:47
1
$begingroup$
en.wikipedia.org/wiki/Conjugacy_class
$endgroup$
– Lord Shark the Unknown
Jan 1 at 18:52
3
$begingroup$
I think you probably need to do some work on basic group theory concepts before trying to apply them.
$endgroup$
– Mark Bennet
Jan 1 at 19:04
1
$begingroup$
Start by looking up the word "conjugacy" in the text. How were you planning on solving the problem if you don't know what it means?
$endgroup$
– anomaly
Jan 1 at 20:38
|
show 1 more comment
1
$begingroup$
Which book are you using? Please edit the question to include the details.
$endgroup$
– Shaun
Jan 1 at 18:44
$begingroup$
For any $sigmain A_5$, the conjugacy map $c_sigma:A_5to A_5$ is defined by $c_sigma(tau)=sigma^{-1}tausigma$ for each $tauin A_5$.
$endgroup$
– Shaun
Jan 1 at 18:47
1
$begingroup$
en.wikipedia.org/wiki/Conjugacy_class
$endgroup$
– Lord Shark the Unknown
Jan 1 at 18:52
3
$begingroup$
I think you probably need to do some work on basic group theory concepts before trying to apply them.
$endgroup$
– Mark Bennet
Jan 1 at 19:04
1
$begingroup$
Start by looking up the word "conjugacy" in the text. How were you planning on solving the problem if you don't know what it means?
$endgroup$
– anomaly
Jan 1 at 20:38
1
1
$begingroup$
Which book are you using? Please edit the question to include the details.
$endgroup$
– Shaun
Jan 1 at 18:44
$begingroup$
Which book are you using? Please edit the question to include the details.
$endgroup$
– Shaun
Jan 1 at 18:44
$begingroup$
For any $sigmain A_5$, the conjugacy map $c_sigma:A_5to A_5$ is defined by $c_sigma(tau)=sigma^{-1}tausigma$ for each $tauin A_5$.
$endgroup$
– Shaun
Jan 1 at 18:47
$begingroup$
For any $sigmain A_5$, the conjugacy map $c_sigma:A_5to A_5$ is defined by $c_sigma(tau)=sigma^{-1}tausigma$ for each $tauin A_5$.
$endgroup$
– Shaun
Jan 1 at 18:47
1
1
$begingroup$
en.wikipedia.org/wiki/Conjugacy_class
$endgroup$
– Lord Shark the Unknown
Jan 1 at 18:52
$begingroup$
en.wikipedia.org/wiki/Conjugacy_class
$endgroup$
– Lord Shark the Unknown
Jan 1 at 18:52
3
3
$begingroup$
I think you probably need to do some work on basic group theory concepts before trying to apply them.
$endgroup$
– Mark Bennet
Jan 1 at 19:04
$begingroup$
I think you probably need to do some work on basic group theory concepts before trying to apply them.
$endgroup$
– Mark Bennet
Jan 1 at 19:04
1
1
$begingroup$
Start by looking up the word "conjugacy" in the text. How were you planning on solving the problem if you don't know what it means?
$endgroup$
– anomaly
Jan 1 at 20:38
$begingroup$
Start by looking up the word "conjugacy" in the text. How were you planning on solving the problem if you don't know what it means?
$endgroup$
– anomaly
Jan 1 at 20:38
|
show 1 more comment
1 Answer
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$begingroup$
The conjugacy class $[tau]_{A_5}$ of $tauin A_5$ is defined by $$[tau]_{A_5}:={c_sigma(tau)mid sigmain A_5},$$ where $$begin{align} c_sigma: A_5 &to A_5, \ pi &mapsto sigma^{-1}pisigmaend{align}$$ is the conjugacy map.
answered Jan 1 at 18:53
ShaunShaun
8,818113681
$endgroup$
add a comment |
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1 Answer
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$begingroup$
The conjugacy class $[tau]_{A_5}$ of $tauin A_5$ is defined by $$[tau]_{A_5}:={c_sigma(tau)mid sigmain A_5},$$ where $$begin{align} c_sigma: A_5 &to A_5, \ pi &mapsto sigma^{-1}pisigmaend{align}$$ is the conjugacy map.
answered Jan 1 at 18:53
ShaunShaun
8,818113681
$endgroup$
add a comment |
$begingroup$
The conjugacy class $[tau]_{A_5}$ of $tauin A_5$ is defined by $$[tau]_{A_5}:={c_sigma(tau)mid sigmain A_5},$$ where $$begin{align} c_sigma: A_5 &to A_5, \ pi &mapsto sigma^{-1}pisigmaend{align}$$ is the conjugacy map.
answered Jan 1 at 18:53
ShaunShaun
8,818113681
$endgroup$
add a comment |
$begingroup$
The conjugacy class $[tau]_{A_5}$ of $tauin A_5$ is defined by $$[tau]_{A_5}:={c_sigma(tau)mid sigmain A_5},$$ where $$begin{align} c_sigma: A_5 &to A_5, \ pi &mapsto sigma^{-1}pisigmaend{align}$$ is the conjugacy map.
answered Jan 1 at 18:53
ShaunShaun
8,818113681
$endgroup$
The conjugacy class $[tau]_{A_5}$ of $tauin A_5$ is defined by $$[tau]_{A_5}:={c_sigma(tau)mid sigmain A_5},$$ where $$begin{align} c_sigma: A_5 &to A_5, \ pi &mapsto sigma^{-1}pisigmaend{align}$$ is the conjugacy map.
answered Jan 1 at 18:53
ShaunShaun
8,818113681
answered Jan 1 at 18:53
ShaunShaun
8,818113681
answered Jan 1 at 18:53
ShaunShaun
8,818113681
answered Jan 1 at 18:53
ShaunShaun
8,818113681
8,818113681
add a comment |
add a comment |
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1
$begingroup$
Which book are you using? Please edit the question to include the details.
$endgroup$
– Shaun
Jan 1 at 18:44
$begingroup$
For any $sigmain A_5$, the conjugacy map $c_sigma:A_5to A_5$ is defined by $c_sigma(tau)=sigma^{-1}tausigma$ for each $tauin A_5$.
$endgroup$
– Shaun
Jan 1 at 18:47
1
$begingroup$
en.wikipedia.org/wiki/Conjugacy_class
$endgroup$
– Lord Shark the Unknown
Jan 1 at 18:52
3
$begingroup$
I think you probably need to do some work on basic group theory concepts before trying to apply them.
$endgroup$
– Mark Bennet
Jan 1 at 19:04
1
$begingroup$
Start by looking up the word "conjugacy" in the text. How were you planning on solving the problem if you don't know what it means?
$endgroup$
– anomaly
Jan 1 at 20:38