Category:Symmetric Groups
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This category contains results about Symmetric Groups.
Definitions specific to this category can be found in Definitions/Symmetric Groups.
Let $S$ be a set.
Let $\map \Gamma S$ denote the set of permutations on $S$.
Let $\struct {\map \Gamma S, \circ}$ be the algebraic structure such that $\circ$ denotes the composition of mappings.
Then $\struct {\map \Gamma S, \circ}$ is called the symmetric group on $S$.
If $S$ has $n$ elements, then $\struct {\map \Gamma S, \circ}$ is often denoted $S_n$.
Subcategories
This category has the following 17 subcategories, out of 17 total.
A
C
E
G
P
S
- Sign of Permutation (3 P)
- Symmetric Group is Group (3 P)
T
- Transitive Subgroups (3 P)
Pages in category "Symmetric Groups"
The following 62 pages are in this category, out of 62 total.
A
C
E
G
I
N
P
- Parity Function is Homomorphism
- Parity of Conjugate of Permutation
- Parity of Inverse of Permutation
- Permutation Group is Subgroup of Symmetric Group
- Permutation Induces Equivalence Relation
- Permutation Induces Equivalence Relation/Corollary
- Permutation of Cosets
- Permutation of Cosets/Corollary 1
- Permutation of Cosets/Corollary 2
- Power of Moved Element is Moved
- Powers of Disjoint Permutations
- Powers of Permutation Element
S
- Set of Invertible Mappings forms Symmetric Group
- Set of Transpositions is not Subgroup of Symmetric Group
- Sign of Permutation is Plus or Minus Unity
- Stabilizer in Group of Transformations
- Subgroup of Symmetric Group that Fixes n
- Subgroups of Symmetric Group Isomorphic to Product of Subgroups
- Symmetric Group has Non-Normal Subgroup
- Symmetric Group is Generated by Transposition and n-Cycle
- Symmetric Group is Group
- Symmetric Group is not Abelian
- Symmetric Group is Subgroup of Monoid of Self-Maps
- Symmetric Group on Greater than 4 Letters is Not Solvable
- Symmetric Group on n Letters is Isomorphic to Symmetric Group
- Symmetric Groups of Same Order are Isomorphic