GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory/NumSimpleGroups

GroupTheory

  

NumSimpleGroups

  

return the number of simple groups of a given finite order

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

NumSimpleGroups( n )

Parameters

n

-

a positive integer; usually, the order of a finite simple group

Description

• 

For a positive integer n, the NumSimpleGroups( n ) command returns the number of simple groups of order n.

• 

For each prime integer n, the number of simple groups of order n is equal to 1. By the Feit-Thompson Theorem, if n is an odd composite integer, there are no simple groups of order n. The Artin-Tits theorem asserts that the number of simple groups of any given finite order is at most equal to 2. Therefore, the value returned by NumSimpleGroups( n ), for any positive integer n, is one of 0, 1 or 2.

Examples

withGroupTheory:

NumSimpleGroups1

0

(1)

NumSimpleGroups13

1

(2)

NumSimpleGroups15

0

(3)

NumSimpleGroups360

1

(4)

NumSimpleGroups20160

2

(5)

Compatibility

• 

The GroupTheory[NumSimpleGroups] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

GroupTheory[ClassifyFiniteSimpleGroup]

GroupTheory[IsSimple]

GroupTheory[IsSimpleNumber]