'Test if the group is nilpotent.
A group `G` is nilpotent if it has a central series of finite length.
Alternatively, `G` is nilpotent if its lower central series terminates
with the trivial group. Every nilpotent group is also solvable
([1], p.29, [12]).
Examples
>>> from sympy.combinatorics.named_groups import (SymmetricGroup,
... CyclicGroup)
>>> C = CyclicGroup(6)
>>> C.is_nilpotent
True
>>> S = SymmetricGroup(5)
>>> S.is_nilpotent
False
See Also
lower_central_series, is_solvable'

@property
def is_nilpotent(self):

    if (self._is_nilpotent is None):
        lcs = self.lower_central_series()
        terminator = lcs[(len(lcs) - 1)]
        gens = terminator.generators
        degree = self.degree
        identity = _af_new(list(range(degree)))
        if all(((g == identity) for g in gens)):
            self._is_solvable = True
            self._is_nilpotent = True
            return True
        else:
            self._is_nilpotent = False
            return False
    else:
        return self._is_nilpotent
