quotient_group(u)

Returns the residue class group of the normal subgroup u.
separate

Returns the subgroup whose elements makes the block true.
to_a

Returns the array of elements. The first is the unity.
unity

Returns the unity.
unit_group

Returns the unit group.
semi_complete!

Makes self be the semigroup generated by the elements.
semi_complete

Returns the semigroup generated by the elements.
complete!

Makes self be the semigroup generated by the elements.
complete

Returns the group generated by the elements.
closed?

Returns true when self is closed by product and inverse.
subgroups

Returns the all subgroups.
centralizer(s)

Returns the centralize of s in self.
center

Returns the center ofself.
center?(x)

Returns true if x is in the center of self.
normalizer(s)

Returns the normalizer of s in self.
normal?(s)

Returns true if s is a normal subgroup of self.
normal_subgroups

Returns the all normal subgroups.
conjugacy_class(x)

Returns the conjugacy class of the element x.
conjugacy_classes

Returns the set of all conjucacy claases of self.
simple?

Retuns true if self is a simple group.
commutator([h])

Returns the commutator subgroup of self and h.
If the parameter is omitted, h is assumed to be self.
D([n])

Returns the nthe commutator subgroup.
D(0) = self
and D(n+1) = [D[n], D[n]]
.
If the parameter ommitted, n is assumed to be 1.
commutator_series

Returns the array [D(0), D(1), D(2),..., D(n)]
.
This sequence is terminated for n with D(n) == D(n+1)
.
solvable?

Returns true if self is solvable.
K([n])

Returns the subgroup definend such that K(0) = self
and
K(n+1) = [self, K[n]
.
If the parameter is omitted, n is asumed to be 1.
descending_central_series

Returns the descending central series:
[K(0), K(1), K(2),..., K(n)]
.
This sequence is terminated for n with K(n) == K(n+1)
.
Z([n])

Returns the subgroup that defined by: Z(0) = unit group
,
Z(n+1) = separate{x commutator(Set[x]) <= Z(n1)}
.
If the parameter is omitted, n is assumed to be 1.
ascending_central_series

Returns the array of ascending central series:
[Z(0), Z(1), Z(2),..., Z(n)]
.
This sequence is terminated for n such that
Z(n) == Z(n+1)
.
nilpotent?

Returns true if self is nilpotent.
nilpotency_class

Returns the class of nilpotency.
If self is not nilpotent, returns nil.