All permutations carrying the set {1,2} into the set {1,2}
$begingroup$
Book question:
Describe the following subgroups of $S_4$ and determine the number of elements in each subgroup:
a) All permutations carrying the set {1,2} into the set {1,2}
My question:
What does it mean by carrying the set {1,2} into the set {1,2}?
I assume it means permutations such as (12) and (12)(34), but would it also include (123) (which I sort of doubt because 2 $rightarrow$ 3 and 3 $notin$ {1,2}) or permutations where 1 and 2 don't permute, such as (34) = (1)(2)(34)?
abstract-algebra terminology permutation-cycles
edited Dec 24 '18 at 18:58
Shaun
9,083113683
asked Nov 5 '18 at 6:31
JayJay
11
$endgroup$
add a comment |
$begingroup$
Book question:
Describe the following subgroups of $S_4$ and determine the number of elements in each subgroup:
a) All permutations carrying the set {1,2} into the set {1,2}
My question:
What does it mean by carrying the set {1,2} into the set {1,2}?
I assume it means permutations such as (12) and (12)(34), but would it also include (123) (which I sort of doubt because 2 $rightarrow$ 3 and 3 $notin$ {1,2}) or permutations where 1 and 2 don't permute, such as (34) = (1)(2)(34)?
abstract-algebra terminology permutation-cycles
edited Dec 24 '18 at 18:58
Shaun
9,083113683
asked Nov 5 '18 at 6:31
JayJay
11
$endgroup$
$begingroup$
I'm sure it means the $sigmain S_4$ with $sigma(A)=A$ where $A={1,2}$. Also, please see math.meta.stackexchange.com/questions/5020
$endgroup$
– Lord Shark the Unknown
Nov 5 '18 at 6:40
add a comment |
$begingroup$
Book question:
Describe the following subgroups of $S_4$ and determine the number of elements in each subgroup:
a) All permutations carrying the set {1,2} into the set {1,2}
My question:
What does it mean by carrying the set {1,2} into the set {1,2}?
I assume it means permutations such as (12) and (12)(34), but would it also include (123) (which I sort of doubt because 2 $rightarrow$ 3 and 3 $notin$ {1,2}) or permutations where 1 and 2 don't permute, such as (34) = (1)(2)(34)?
abstract-algebra terminology permutation-cycles
edited Dec 24 '18 at 18:58
Shaun
9,083113683
asked Nov 5 '18 at 6:31
JayJay
11
$endgroup$
Book question:
Describe the following subgroups of $S_4$ and determine the number of elements in each subgroup:
a) All permutations carrying the set {1,2} into the set {1,2}
My question:
What does it mean by carrying the set {1,2} into the set {1,2}?
I assume it means permutations such as (12) and (12)(34), but would it also include (123) (which I sort of doubt because 2 $rightarrow$ 3 and 3 $notin$ {1,2}) or permutations where 1 and 2 don't permute, such as (34) = (1)(2)(34)?
abstract-algebra terminology permutation-cycles
abstract-algebra terminology permutation-cycles
edited Dec 24 '18 at 18:58
Shaun
9,083113683
asked Nov 5 '18 at 6:31
JayJay
11
edited Dec 24 '18 at 18:58
Shaun
9,083113683
asked Nov 5 '18 at 6:31
JayJay
11
edited Dec 24 '18 at 18:58
Shaun
9,083113683
edited Dec 24 '18 at 18:58
Shaun
9,083113683
edited Dec 24 '18 at 18:58
Shaun
9,083113683
9,083113683
asked Nov 5 '18 at 6:31
JayJay
11
asked Nov 5 '18 at 6:31
JayJay
11
asked Nov 5 '18 at 6:31
JayJay
11
11
$begingroup$
I'm sure it means the $sigmain S_4$ with $sigma(A)=A$ where $A={1,2}$. Also, please see math.meta.stackexchange.com/questions/5020
$endgroup$
– Lord Shark the Unknown
Nov 5 '18 at 6:40
add a comment |
$begingroup$
I'm sure it means the $sigmain S_4$ with $sigma(A)=A$ where $A={1,2}$. Also, please see math.meta.stackexchange.com/questions/5020
$endgroup$
– Lord Shark the Unknown
Nov 5 '18 at 6:40
$begingroup$
I'm sure it means the $sigmain S_4$ with $sigma(A)=A$ where $A={1,2}$. Also, please see math.meta.stackexchange.com/questions/5020
$endgroup$
– Lord Shark the Unknown
Nov 5 '18 at 6:40
$begingroup$
I'm sure it means the $sigmain S_4$ with $sigma(A)=A$ where $A={1,2}$. Also, please see math.meta.stackexchange.com/questions/5020
$endgroup$
– Lord Shark the Unknown
Nov 5 '18 at 6:40
add a comment |
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$begingroup$
I'm sure it means the $sigmain S_4$ with $sigma(A)=A$ where $A={1,2}$. Also, please see math.meta.stackexchange.com/questions/5020
$endgroup$
– Lord Shark the Unknown
Nov 5 '18 at 6:40