Strong generating set

In abstract algebra, especially in the area of group theory, a strong generating set of a permutation group is a generating set that clearly exhibits the permutation structure as described by a stabilizer chain. A stabilizer chain is a sequence of subgroups, each containing the next and each stabilizing one more point.
Let formula_1 be a group of permutations of the set formula_2 Let 
be a sequence of distinct integers, formula_4 such that the pointwise stabilizer of formula_5 is trivial (i.e., let formula_5 be a base for formula_7). Define 
and define formula_9 to be the pointwise stabilizer of formula_10. A strong generating set (SGS) for G relative to the base formula_5 is a set 
such that 
for each formula_14 such that formula_15.
The base and the SGS are said to be non-redundant if 
for formula_17.
A base and strong generating set (BSGS) for a group can be computed using the Schreier–Sims algorithm.