'Return a chain of stabilizers relative to a base and strong generating
set.
The ``i``-th basic stabilizer `G^{(i)}` relative to a base
`(b_1, b_2, ..., b_k)` is `G_{b_1, b_2, ..., b_{i-1}}`. For more
information, see [1], pp. 87-89.
Examples
>>> from sympy.combinatorics.named_groups import AlternatingGroup
>>> A = AlternatingGroup(4)
>>> A.schreier_sims()
>>> A.base
[0, 1]
>>> for g in A.basic_stabilizers:
...     print(g)
PermutationGroup([
(3)(0 1 2),
(1 2 3)])
PermutationGroup([
(1 2 3)])
See Also
base, strong_gens, basic_orbits, basic_transversals'

@property
def basic_stabilizers(self):

    if (self._transversals == []):
        self.schreier_sims()
    strong_gens = self._strong_gens
    base = self._base
    if (not base):
        return []
    strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
    basic_stabilizers = []
    for gens in strong_gens_distr:
        basic_stabilizers.append(PermutationGroup(gens))
    return basic_stabilizers
