Base (group theory)
Let be a finite permutation group acting on a set
. A sequence
of k distinct elements of is a base for G if the only element of
which fixes every
pointwise is the identity element of
.[1]
Bases and strong generating sets are concepts of importance in computational group theory. A base and a strong generating set (together often called a BSGS) for a group can be obtained using the Schreier–Sims algorithm.[2]
It is often beneficial to deal with bases and strong generating sets as these may be easier to work with than the entire group. A group may have a small base compared to the set it acts on. In the "worst case", the symmetric groups and alternating groups have large bases (the symmetric group Sn has base size n − 1), and there are often specialized algorithms that deal with these cases.
References
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