Strong generating set

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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 (i.e., let be a base for ). Define

and define to be the pointwise stabilizer of . A strong generating set (SGS) 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 (BSGS) for a group can be computed using the Schreier–Sims algorithm.


References[edit]

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