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GroupTheory

  

FrobeniusProduct

  

compute the product of two complexes in a finite group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

FrobeniusProduct( A, B, G )

ComplexProduct( A, B, G )

Parameters

A

-

a subset of G

B

-

a subset of G

G

-

a group

Description

• 

The Frobenius product of two complexes A and B in a group G is the set of all elements ab, with aA and bB.

• 

The  FrobeniusProduct( A, B, G ) command computes the product of the complexes A and B in the finite group G.

• 

The ComplexProduct command is provided as an alias.

Examples

withGroupTheory:

GAlt4

GA4

(1)

APerm1,2,4,Perm1,2,3,4

A1,2,4,1,23,4

(2)

BPerm1,2,3,Perm2,3,4,Perm1,3,2,4

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

(3)

CFrobeniusProductA,B,G

C1,4,3,1,3,4,1,42,3,1,3,2,1,32,4

(4)

nopsCnopsAnopsB

56

(5)

AConjugacyClassPerm1,2,3,4,G

A1,23,4A4

(6)

BConjugacyClassPerm1,2,4,G

B1,2,4A4

(7)

Note that you must compute the elements of these conjugacy classes before computing their complex product.

CFrobeniusProductElementsA,ElementsB,G

C1,4,3,1,3,2,1,2,4,2,3,4

(8)

numelemsC

4

(9)

numelemsAnumelemsB

12

(10)

Compatibility

• 

The GroupTheory[FrobeniusProduct] command was introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

GroupTheory

GroupTheory[ConjugacyClass]

GroupTheory[Elements]

numelems

Perm