Question on alternating groups [closed]
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An alternating group is the group of even permutations of a finite set.
Question : Is there any theorem like $G$ is an alternating group iff something..
I tried on internet, but did not get anything.
group-theory symmetric-groups
asked Nov 16 at 12:08
I_wil_break_wall
163
closed as too broad by Brahadeesh, Lord Shark the Unknown, Parcly Taxel, John B, amWhy Nov 17 at 12:08
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
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An alternating group is the group of even permutations of a finite set.
Question : Is there any theorem like $G$ is an alternating group iff something..
I tried on internet, but did not get anything.
group-theory symmetric-groups
asked Nov 16 at 12:08
I_wil_break_wall
163
closed as too broad by Brahadeesh, Lord Shark the Unknown, Parcly Taxel, John B, amWhy Nov 17 at 12:08
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$A_n$ is the commutator subgroup of $S_n$: math.stackexchange.com/questions/1501395/…
– mathnoob
Nov 16 at 12:31
Also: For $n>3$, except $n=6$, the automorphism group of $A_n$ is the symmetric group $S_n$ with inner automorphism group $A_n$. en.wikipedia.org/wiki/Alternating_group
– mathnoob
Nov 16 at 12:41
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up vote
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up vote
0
down vote
favorite
An alternating group is the group of even permutations of a finite set.
Question : Is there any theorem like $G$ is an alternating group iff something..
I tried on internet, but did not get anything.
group-theory symmetric-groups
asked Nov 16 at 12:08
I_wil_break_wall
163
An alternating group is the group of even permutations of a finite set.
Question : Is there any theorem like $G$ is an alternating group iff something..
I tried on internet, but did not get anything.
group-theory symmetric-groups
group-theory symmetric-groups
asked Nov 16 at 12:08
I_wil_break_wall
163
asked Nov 16 at 12:08
I_wil_break_wall
163
asked Nov 16 at 12:08
I_wil_break_wall
163
asked Nov 16 at 12:08
I_wil_break_wall
163
asked Nov 16 at 12:08
I_wil_break_wall
163
163
closed as too broad by Brahadeesh, Lord Shark the Unknown, Parcly Taxel, John B, amWhy Nov 17 at 12:08
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as too broad by Brahadeesh, Lord Shark the Unknown, Parcly Taxel, John B, amWhy Nov 17 at 12:08
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$A_n$ is the commutator subgroup of $S_n$: math.stackexchange.com/questions/1501395/…
– mathnoob
Nov 16 at 12:31
Also: For $n>3$, except $n=6$, the automorphism group of $A_n$ is the symmetric group $S_n$ with inner automorphism group $A_n$. en.wikipedia.org/wiki/Alternating_group
– mathnoob
Nov 16 at 12:41
add a comment |
$A_n$ is the commutator subgroup of $S_n$: math.stackexchange.com/questions/1501395/…
– mathnoob
Nov 16 at 12:31
Also: For $n>3$, except $n=6$, the automorphism group of $A_n$ is the symmetric group $S_n$ with inner automorphism group $A_n$. en.wikipedia.org/wiki/Alternating_group
– mathnoob
Nov 16 at 12:41
$A_n$ is the commutator subgroup of $S_n$: math.stackexchange.com/questions/1501395/…
– mathnoob
Nov 16 at 12:31
$A_n$ is the commutator subgroup of $S_n$: math.stackexchange.com/questions/1501395/…
– mathnoob
Nov 16 at 12:31
Also: For $n>3$, except $n=6$, the automorphism group of $A_n$ is the symmetric group $S_n$ with inner automorphism group $A_n$. en.wikipedia.org/wiki/Alternating_group
– mathnoob
Nov 16 at 12:41
Also: For $n>3$, except $n=6$, the automorphism group of $A_n$ is the symmetric group $S_n$ with inner automorphism group $A_n$. en.wikipedia.org/wiki/Alternating_group
– mathnoob
Nov 16 at 12:41
add a comment |
1 Answer
1
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I can't guess what you have in mind, so here's "something":
A group $G$ such that $|G|>4$ is isomorphic to an alternating group if and only if $G$ is a proper normal subgroup of some symmetric group.
answered Nov 16 at 12:33
the_fox
2,1421429
2
I think you could make that $|G|>4$.
– Derek Holt
Nov 16 at 12:50
Yes, you are right!
– the_fox
Nov 16 at 13:12
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
I can't guess what you have in mind, so here's "something":
A group $G$ such that $|G|>4$ is isomorphic to an alternating group if and only if $G$ is a proper normal subgroup of some symmetric group.
answered Nov 16 at 12:33
the_fox
2,1421429
2
I think you could make that $|G|>4$.
– Derek Holt
Nov 16 at 12:50
Yes, you are right!
– the_fox
Nov 16 at 13:12
add a comment |
up vote
0
down vote
I can't guess what you have in mind, so here's "something":
A group $G$ such that $|G|>4$ is isomorphic to an alternating group if and only if $G$ is a proper normal subgroup of some symmetric group.
answered Nov 16 at 12:33
the_fox
2,1421429
2
I think you could make that $|G|>4$.
– Derek Holt
Nov 16 at 12:50
Yes, you are right!
– the_fox
Nov 16 at 13:12
add a comment |
up vote
0
down vote
up vote
0
down vote
I can't guess what you have in mind, so here's "something":
A group $G$ such that $|G|>4$ is isomorphic to an alternating group if and only if $G$ is a proper normal subgroup of some symmetric group.
answered Nov 16 at 12:33
the_fox
2,1421429
I can't guess what you have in mind, so here's "something":
A group $G$ such that $|G|>4$ is isomorphic to an alternating group if and only if $G$ is a proper normal subgroup of some symmetric group.
answered Nov 16 at 12:33
the_fox
2,1421429
edited Nov 16 at 13:13
answered Nov 16 at 12:33
the_fox
2,1421429
answered Nov 16 at 12:33
the_fox
2,1421429
answered Nov 16 at 12:33
the_fox
2,1421429
2,1421429
2
I think you could make that $|G|>4$.
– Derek Holt
Nov 16 at 12:50
Yes, you are right!
– the_fox
Nov 16 at 13:12
add a comment |
2
I think you could make that $|G|>4$.
– Derek Holt
Nov 16 at 12:50
Yes, you are right!
– the_fox
Nov 16 at 13:12
2
2
I think you could make that $|G|>4$.
– Derek Holt
Nov 16 at 12:50
I think you could make that $|G|>4$.
– Derek Holt
Nov 16 at 12:50
Yes, you are right!
– the_fox
Nov 16 at 13:12
Yes, you are right!
– the_fox
Nov 16 at 13:12
add a comment |
$A_n$ is the commutator subgroup of $S_n$: math.stackexchange.com/questions/1501395/…
– mathnoob
Nov 16 at 12:31
Also: For $n>3$, except $n=6$, the automorphism group of $A_n$ is the symmetric group $S_n$ with inner automorphism group $A_n$. en.wikipedia.org/wiki/Alternating_group
– mathnoob
Nov 16 at 12:41