Algorithm for Normalizing Generator Input: a permutation group H with base B=[~I ,~2, -.-., 13k], strong generating set T, Schreier vectors v t~ , and basic orbits A (i) ; a permutation y normalizing H; Output: a base for K = which may extend B; a sequence of elements [g 1 ,g 2 ..... gr] such that, for each j, (a) T L.) {gj,gj+l ..... gr } is a strong generating set of , (b) gj ~ , (c) gi normalizes , and (d) gp ~ , for some prime pj;

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