Strong generating set

Let $$G leq S_n be a permutation group. Let

:$$B = (eta_1, eta_2, ldots, eta_r)

be a sequence of distinct integers, $$eta_i in { 1, 2, ldots, n } , such that the pointwise stabilizer of $$B is trivial (ie: let $$B be a base for $$G ). Define

:$$B_i = (eta_1, eta_2, ldots, eta_i) ,

and define $$G^{(i)} to be the pointwise stabilizer of $$B_i . A strong generating set (SGS) for G relative to the base $$B is a set

:$$S subset G

such that

:$$langle S cap G^{(i)} angle = G^{(i)}

for each $$1 leq i leq r .

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

:$$G^{(i)} eq G^{(j)}

for $$i eq j .

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