Category:Conjugacy
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This category contains results about Conjugacy in the context of Group Theory.
Definitions specific to this category can be found in Definitions/Conjugacy.
Let $\struct {G, \circ}$ be a group.
Definition 1
The conjugacy relation $\sim$ is defined on $G$ as:
- $\forall \tuple {x, y} \in G \times G: x \sim y \iff \exists a \in G: a \circ x = y \circ a$
Definition 2
The conjugacy relation $\sim$ is defined on $G$ as:
- $\forall \tuple {x, y} \in G \times G: x \sim y \iff \exists a \in G: a \circ x \circ a^{-1} = y$
Subcategories
This category has the following 7 subcategories, out of 7 total.
Pages in category "Conjugacy"
The following 32 pages are in this category, out of 32 total.
C
- Conjugacy Class Equation
- Conjugacy is Equivalence Relation
- Conjugate of Commuting Elements
- Conjugate of Cycle
- Conjugate of Set by Group Product
- Conjugate of Set by Identity
- Conjugate of Set with Inverse Closed for Inverses
- Conjugate of Set with Inverse is Closed
- Conjugate of Subgroup is Subgroup
- Conjugate Permutations have Same Cycle Type
- Conjugates of Elements in Centralizer
- Cycle Decomposition of Conjugate
E
N
O
S
- Subgroup equals Conjugate iff Normal
- Subgroup is Normal iff Contains Conjugate Elements
- Subgroup is Normal iff Left Coset Space is Right Coset Space
- Subgroup is Normal iff Left Cosets are Right Cosets
- Subgroup is Normal iff Normal Subset
- Subgroup is Subset of Conjugate iff Normal
- Subgroup is Superset of Conjugate iff Normal
- Subset has 2 Conjugates then Normal Subgroup