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 be a group of permutations of the set Let
be a sequence of distinct integers, such that the pointwise stabilizer of is trivial. Define
and define to be the pointwise stabilizer of. A strong generating set for G relative to the base is a set
such that
for each such that.
The base and the SGS are said to be non-redundant if
for.
A base and strong generating set for a group can be computed using the Schreier–Sims algorithm.
