Strong generating set

Let $G\; leq\; S\_n$ be a permutation group. Let

:

be a sequence of distinct integers, , such that the pointwise stabilizer of $B$ is trivial (ie: let $B$ be a base for $G$). Define

:,

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.