Is there some basis containing polynomials of the form x[1]^p*x[2]^q+x[2]^p*x[3]^q+x[3]^p*x[1]^q, (p,q posint)?
Are there known relationships between these?

Note: these are not the symmetric polynomials.

How does one view procedures not listed for export in modules?

Given  3000 linear equations in 3000 unknowns, with coefficients in a field of rationals with one algebraic number extension, which Maple solver would be fastest in solving the system?

with(GroupTheory):
MinimumPermutationRepresentationDegree(PermutationGroup({[[2, 3], [4, 5]], [[2, 5], [3, 4]]}, degree = 5, supergroup = PermutationGroup({[[2, 3, 4]], [[1, 2], [4, 5]]}, degree = 5)));

#an error appears in Maple 2017
 

Is there a Maple function that given a group gives its name?