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3 Residual Functions

  • ResidualWrtFormation( G, F ) O

    Let G be a finite solvable group and F a formation. Then ResidualWrtFormation returns the F-residual subgroup of G.

    The following special cases have their own functions.

  • NilpotentResidual( G ) A

    This is the last term of the descending central series of G.

  • PResidual( G, p ) O

    This is the smallest normal subgroup of G whose index is a power of the prime p.

  • PiResidual( G, primes ) O

    This is the smallest normal subgroup of G whose index is divisible only by primes in the list primes.

  • CoprimeResidual( G, primes ) O

    This is the smallest normal subgroup of G whose index is divisible only by primes not in the list primes.

  • ElementaryAbelianProductResidual( G ) A

    This is the smallest normal subgroup of G whose factor group is a direct product of groups of prime order.

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    November 2011