COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

54 H. Jiirgensen Calculation with elements of a finite group 55
It is important here that the multiplication algorithm is defined for
seminormed words as left factors. For computing jail (i = l(l)n) M* is used.
4.6. M developedfrom M*. What proved to be most time-consuming%
that with an AG-system given the number of steps to be taken for norming
the word aia%&sj-l I 3 1” .a> will in general increase rather fast, when Sj is
increased.
As a remedy further normed words h, = [ai, a:] (1 e i -= j 5 n;
2 == k-= vi> are introduced, if there exist i and j (1 e i-=j=sn) such that
vj + 2 and gii + e. For computing these normed words M* is used.
In M* norming a,u,dra$:;. . .a? for i-=j and 6j>l is based on the equation
aiais,& 8,-l 6,-I
a1‘I = ajaigija,
. . . C7j-l . . . a$.
The subroutines P(i, j, k) of M* for i