Sage and Groups

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Section B.1 Sage and Groups

“A sage is the instructor of a hundred ages.”
―Ralph Waldo Emerson

Subsection Sage and Groups

A brief and non-exhaustive list of groups:

Abelian Groups.
The command
```
AbelianGroup([n])
```
generates an abelian group of order $n$ (using $n=0$ yields $\Z$)
```
G = AbelianGroup([n])
```

G = SymmetricGroup(n)

and

G = AlternatingGroup(n)

```
G = DihedralGroup(n)
```
```
G = CyclicPermutationGroup(n)
```

Here we have a list

.is_abelian(), .is_finite(), .is_multiplicative(), .is_trivial(), .order()

Subsection Sage and Finitely Presented Groups

Recall that all groups can be constructed as quotients of free groups.

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