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GroupTheory

  

FreeGroup

  

construct a free group of given rank or on a specified basis

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

FreeGroup( n )

FreeGroup( B )

Parameters

n

-

nonnegint: the rank of the free group

B

-

{set,list}(symbol) : a set or list of symbols specifying a basis

Description

• 

A free group is a group that has a free basis, which is a set B for which the group has the presentation with B as generators and an empty set of relators. The number of elements in a basis B is called the rank of the free group.

• 

The FreeGroup( n ) command returns a free group, as a finitely presented group, of rank n.

• 

The FreeGroup( B ) command returns a free group with the member of the set or list B of names as basis. Its rank is therefore the number of elements in B.

• 

Note that a free group of rank 0 is trivial, and a free group of rank 1 is an infinite cyclic group. Free groups with rank greater than 1 are non-abelian.

Examples

withGroupTheory:

FreeGroup2

_x1,_x2

(1)

FFreeGroupa,b,c

Fa,b,c

(2)

GeneratorsF

a,b,c

(3)

GroupOrderF

(4)

IsAbelianF

false

(5)

IsAbelianFreeGroup1

true

(6)

latexFreeGroup2k

\mathrm{F}_{2\,k}

Compatibility

• 

The GroupTheory[FreeGroup] command was introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

GroupTheory

GroupTheory[FPGroup]

GroupTheory[Generators]

GroupTheory[GroupOrder]

GroupTheory[IsAbelian]