# Category:Commutativity

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This category contains results about **commutativity**.

Definitions specific to this category can be found in Definitions/Commutativity.

Let $\circ$ be a binary operation.

Two elements $x, y$ are said to **commute (with each other)** if and only if:

- $x \circ y = y \circ x$

## Subcategories

This category has the following 13 subcategories, out of 13 total.

## Pages in category "Commutativity"

The following 51 pages are in this category, out of 51 total.

### C

- Commutation of Inverses in Monoid
- Commutation Property in Group
- Commutation with Group Elements implies Commuation with Product with Inverse
- Commutation with Inverse in Monoid
- Commutative and Associative Product on Space of Distributions does not Exist
- Commutative Semigroup is Entropic Structure
- Commutativity of Powers in Group
- Commutativity of Powers in Monoid
- Commutativity of Powers in Semigroup
- Conjugate of Commuting Elements
- Count of Commutative Binary Operations on Set
- Count of Commutative Binary Operations with Fixed Identity
- Count of Commutative Binary Operations with Identity
- Count of Commutative Operations on Finite Set which are Closed on Every Subset

### E

### L

### O

- Operation over which Every Commutative Associative Operation is Distributive is either Left or Right Operation
- Operation which is Left Distributive over Every Commutative Associative Operation is Right Operation
- Operation which is Right Distributive over Every Commutative Associative Operation is Left Operation

### P

- Power of Product of Commutative Elements in Group
- Power of Product of Commutative Elements in Monoid
- Power of Product of Commutative Elements in Semigroup
- Power of Product of Commuting Elements in Monoid equals Product of Powers
- Power of Product of Commuting Elements in Semigroup equals Product of Powers
- Power Structure Operation on Set of Singleton Subsets preserves Commutativity
- Powers of Commutative Elements in Groups
- Powers of Commutative Elements in Semigroups
- Powers of Commuting Elements of Monoid Commute
- Powers of Commuting Elements of Semigroup Commute
- Powers of Field Elements Commute
- Powers of Group Element Commute
- Powers of Semigroup Element Commute
- Product of Commuting Elements with Inverses
- Product with Matrix Exponential of Commutative Matrices
- Properties of Inverses of Commuting Elements