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GroupTheory

  

SylowBasis

  

construct a Sylow basis for a finite soluble group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SylowBasis( G )

Parameters

G

-

a soluble permutation group

Description

• 

Let G be a finite soluble group.  A Sylow basis for G is a collection B of Sylow subgroups of G, one for each prime divisor of the order of G, such that PQ=QP, for each pair P,Q of Sylow subgroups in B.

• 

The existence of a Sylow basis for G is equivalent to the solubility of G.

• 

The SylowBasis( G ) command constructs a Sylow basis for the soluble group G. If the group G is not soluble, then an exception is raised. The group G must be an instance of a permutation group.

Examples

withGroupTheory:

GAlt4

GA4

(1)

BSylowBasisG

B1,32,4,1,42,3,1,3,2

(2)

mapGroupOrder,B

4,3

(3)

evalbComplexProductB1,B2,G=ComplexProductB2,B1,G

true

(4)

BSylowBasisDihedralGroup15

B1,10,4,13,72,11,5,14,83,12,6,15,9,1,11,62,12,73,13,84,14,95,15,10,1,42,35,156,147,138,129,11

(5)

mapGroupOrder,B

5,3,2

(6)

SylowBasisPSL4,3

Error, (in SylowBasis) group must be soluble

SylowBasisSymm5

Error, (in SylowBasis) group must be soluble

Compatibility

• 

The GroupTheory[SylowBasis] command was introduced in Maple 2019.

• 

For more information on Maple 2019 changes, see Updates in Maple 2019.

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[IsSoluble]

GroupTheory[SylowSubgroup]