GroupTheory
FrobeniusProduct
compute the product of two complexes in a finite group
Calling Sequence
Parameters
Description
Examples
Compatibility
FrobeniusProduct( A, B, G )
ComplexProduct( A, B, G )
A
-
a subset of G
B
G
a group
The Frobenius product of two complexes A and B in a group G is the set of all elements ab, with a∈A and b∈B.
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.
withGroupTheory:
G≔Alt4
G≔A4
A≔Perm1,2,4,Perm1,2,3,4
A≔1,2,4,1,23,4
B≔Perm1,2,3,Perm2,3,4,Perm1,3,2,4
B≔1,32,4,1,2,3,2,3,4
C≔FrobeniusProductA,B,G
C≔1,4,3,1,3,4,1,42,3,1,3,2,1,32,4
nopsC≠nopsAnopsB
5≠6
A≔ConjugacyClassPerm1,2,3,4,G
A≔1,23,4A4
B≔ConjugacyClassPerm1,2,4,G
B≔1,2,4A4
Note that you must compute the elements of these conjugacy classes before computing their complex product.
C≔FrobeniusProductElementsA,ElementsB,G
C≔1,4,3,1,3,2,1,2,4,2,3,4
numelemsC
4
numelemsAnumelemsB
12
The GroupTheory[FrobeniusProduct] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
See Also
GroupTheory[ConjugacyClass]
GroupTheory[Elements]
numelems
Perm
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