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 Let

be a sequence of distinct integers such that the pointwise stabilizer be a base). Define

. A strong generating set is a set

such that

.

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

.

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

References

• A. Seress, Permutation Group Algorithms, Cambridge University Press, 2002.