SylowSubgroup - Maple Help
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GroupTheory

  

SylowSubgroup

  

construct a Sylow subgroup of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SylowSubgroup( p, G )

Parameters

p

-

a positive rational prime

G

-

a permutation group or Cayley table group

Description

• 

Let  be a finite group, and let  be a positive (rational) prime.  A Sylow -subgroup of  is a maximal -subgroup of  where, by a -subgroup, we mean a subgroup whose order is a power of . The Sylow theorems assert that, for a prime divisor  of the order of a finite group , there is a Sylow -subgroup of  and that all Sylow -subgroups of  are conjugate in .  Moreover, the number of Sylow -subgroups of  is congruent to  modulo .

• 

The SylowSubgroup( p, G ) command constructs a Sylow p-subgroup of a group G. The group G must be an instance of a permutation group or a Cayley table group.

• 

Note that, if p is not a divisor of the order of G, then the trivial subgroup of G is returned.

Examples

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Compatibility

• 

The GroupTheory[SylowSubgroup] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory

GroupTheory[AlternatingGroup]

 


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