High Quality Content by WIKIPEDIA articles! 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 G leq S_n be a permutation group. Let B = (beta_1, beta_2, ldots, beta_r) be a sequence of distinct integers, beta_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 = (beta_1, beta_2, ldots, beta_i),, and define G(i) to be the pointwise stabilizer of Bi. 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)} rangle = G^{(i)} for each 1 leq i leq r . The base and the SGS are said to be non-redundant if G^{(i)} neq G^{(j)} for i neq j . A base and strong generating set (BSGS) for a group can be computed using the Schreier–Sims algorithm.

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