# Category:Examples of Groups

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This category contains examples of **Group**.

A **group** is a semigroup with an identity (that is, a monoid) in which every element has an inverse.

## Subcategories

This category has the following 61 subcategories, out of 61 total.

### A

### D

### E

- Examples of Affine Groups (empty)

### F

- Fischer-Griess Monster (1 P)
- Frieze Groups (1 P)

### G

- Group/Examples/inv x = 1 - x (3 P)
- Groups of Order 100 (1 P)
- Groups of Order 105 (2 P)
- Groups of Order 16 (1 P)
- Groups of Order 17 (empty)
- Groups of Order 21 (2 P)
- Groups of Order 27 (1 P)
- Groups of Order 28 (1 P)
- Groups of Order 30 (6 P)
- Groups of Order 32 (1 P)
- Groups of Order 36 (1 P)
- Groups of Order 40 (1 P)
- Groups of Order 42 (1 P)
- Groups of Order 48 (2 P)
- Groups of Order 54 (1 P)
- Groups of Order 56 (1 P)
- Groups of Order 60 (1 P)
- Groups of Order p^2 (2 P)

### H

### M

### O

- Opposite Groups (5 P)
- Orthogonal Groups (5 P)

### S

- Special Linear Group (6 P)

### T

- Trivial Group (8 P)

## Pages in category "Examples of Groups"

The following 41 pages are in this category, out of 41 total.

### G

- Group Example: x inv c y
- Group of Rationals Modulo One is Group
- Group of Rotations about Fixed Point is not Abelian
- Group/Examples
- Group/Examples/ac, ad+b on Positive Reals by Reals
- Group/Examples/inv x = 1 - x
- Group/Examples/Linear Functions
- Group/Examples/Self-Inverse and Cancellable Elements
- Group/Examples/x+y over 1+xy
- Group/Examples/x+y+2 over Reals
- Group/Examples/x+y+xy over Reals less -1
- Group/Non-Group Examples
- Group/Non-Group Examples/Arbitrary Order 4