GroupTheory
FreeGroup
construct a free group of given rank or on a specified basis
Calling Sequence
Parameters
Description
Examples
Compatibility
FreeGroup( n )
FreeGroup( B )
n
-
nonnegint: the rank of the free group
B
{set,list}(symbol) : a set or list of symbols specifying a basis
A free group is a group that has a free basis, which is a set for which the group has the presentation with as generators and an empty set of relators. The number of elements in a basis is called the rank of the free group.
The FreeGroup( n ) command returns a free group, as a finitely presented group, of rank .
The FreeGroup( B ) command returns a free group with the member of the set or list of names as basis. Its rank is therefore the number of elements in .
Note that a free group of rank is trivial, and a free group of rank is an infinite cyclic group. Free groups with rank greater than are non-abelian.
\mathrm{F}_{2 k}
The GroupTheory[FreeGroup] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
See Also
GroupTheory[FPGroup]
GroupTheory[Generators]
GroupTheory[GroupOrder]
GroupTheory[IsAbelian]
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