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GroupTheory

  

IsPGroup

  

determine whether a group is a p-group, for some prime p

  

PGroupPrime

  

determine the prime for which a group is a p-group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsPGroup( G )

IsPGroup( G, prime = p )

PGroupPrime( G )

Parameters

G

-

a group

p

-

a prime number

Description

• 

A group G is a p-group, for a prime number p, if every member of G has finite order equal to a power of p.

• 

A finite group is a p-group if, and only if, its order is a power of p. A finite p-group is nilpotent.

• 

The IsPGroup( G ) command attempts to determine whether the group G is a p-group, for some prime number p. It returns true if G is a p-group and returns false otherwise.

• 

If the prime = p option is passed, with p an explicit prime number, then IsPGroup( G, prime = p ) checks whether G is a p-group. For example, to check whether G is a 3-group, use the command IsPGroup( G, prime = 3 ).

• 

The PGroupPrime( G ) command returns a prime number p if the group G is a non-trivial p-group.  If Maple can determine that G is a trivial group, then the value FAIL is returned (since the trivial group is a p-group, for all primes p, so the value is not well-defined).  If Maple can determine that G is not a p-group for any prime number p, then an exception is raised.

Examples

withGroupTheory:

GAlt4

GA4

(1)

IsPGroupG

false

(2)

PGroupPrimeG

Error, (in PGroupPrime) group does not have prime-power order

GDihedralGroup8

GD8

(3)

IsPGroupG

true

(4)

IsPGroupG,prime=3

false

(5)

PGroupPrimeG

2

(6)

IsPGroupDihedralGroup5

false

(7)

IsPGroupTrivialGroup

true

(8)

PGroupPrimeTrivialGroup

FAIL

(9)

Compatibility

• 

The GroupTheory[IsPGroup] and GroupTheory[PGroupPrime] commands were introduced in Maple 2018.

• 

For more information on Maple 2018 changes, see Updates in Maple 2018.

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[DihedralGroup]

type/prime