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.

be a group of permutations of the set

Let be a sequence of distinct integers,

such that the pointwise stabilizer of

A strong generating set (SGS) for G relative to the base

The base and the SGS are said to be non-redundant if for

A base and strong generating set (BSGS) for a group can be computed using the Schreier–Sims algorithm.