# Category:Commutativity

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** if and only if:

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

## Subcategories

This category has the following 7 subcategories, out of 7 total.

### E

### I

### U

## Pages in category "Commutativity"

The following 47 pages are in this category, out of 47 total.

### A

### 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 Law of Addition
- Commutative Law of Multiplication
- Commutativity of Powers in Group
- Commutativity of Powers in Monoid
- Commutativity of Powers in Semigroup
- Conjugate of Commuting Elements
- Constant Operation is Commutative
- Count of Commutative Binary Operations on Set
- Count of Commutative Binary Operations with Fixed Identity
- Count of Commutative Binary Operations with Identity

### E

### 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
- 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 Group Element Commute
- Powers of Semigroup Element Commute
- Product of Commuting Elements with Inverses
- Properties of Inverses of Commuting Elements