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Dear Gap Forum,

(This is a duplicate of a message sent 24 hours ago to Gap4 - I apologize

to readers who subscribe to both lists for the repetition - but perhaps a

reader of Gap Forum who does not subscribe to Gap4 can provide help.)

I am teaching a first abstract algebra course (for undergraduates), and

will use Gap in a project written by Loren Larson (on sliding block

puzzles). Last time I

used the project with gap3; now we have installed gap4. In gap3 one can use

the function Factorization to express an element of a group as a product of

group generators. This "black box" (from the point of view of the student)

function worked nicely on the small groups encountered in the project.

Factorization appears to have disappeared from gap4. It is possible to

obtain a "factorization" using the GroupHomomorphismsByImages and

PreImagesRepresentative functions.

Is there another work-around that is less cumbersome for the students (who

won't see homomorphisms for another week or two, and not to the depth

needed to explain what these commands are doing)?

Failing that, how does one use Gap to simplify/rewrite the output of the

PreImagesRepresentative function to obtain a "canonical" product. To wit:

gap> G:=SymmetricGroup(6); Sym( [ 1 .. 6 ] ) gap> r:=(1,2); s:=(1,2,3,4,5,6); (1,2) (1,2,3,4,5,6) gap> K:=Subgroup(G,[r,s]); Group([ (1,2), (1,2,3,4,5,6) ]) gap> F:=FreeGroup("x","y"); <free group on the generators [ x, y ]> gap> hom:=GroupHomomorphismByImagesNC(F,K,GeneratorsOfGroup(F), > GeneratorsOfGroup(K)); [ x, y ] -> [ (1,2), (1,2,3,4,5,6) ] gap> PreImagesRepresentative(hom,(2,3,4)); y^-4*x^-1*y^-2*x^-1*y^-1*x^-1*y^-5*x^-1*y^-1*x^-1*y^-4*x^-1*y^-6*x^-1*y^-2*x^ -1*y^-1*x^-1*y^-5*x^-1*y^-1*x^-1*y^-4*x^-1*y^-2*x^-1*y^-1*x^-1*y^-5*x^-1*y^ -1*x^-2*y^-1*x^-1*y^-1*x^-1*y^-4*x^-1*y^-1*x^-1*y^-1*x^-1*y^-4*x^-1*y^-2*x^ -1*y^-1*x^-1*y^-5*x^-1*y^-1*x^-1*y^-4*x^-1*y^-2*x^-1*y^-1*x^-1*y^-5*x^-1*y^ -1*x^-1*y^-4*x^-1*y^-6*x^-1*y^-2*x^-1*y^-1*x^-1*y^-5*x^-1*y^-1*x^-2*y^-1*x^ -1*y^-1*x^-1*y^-1*x^-1*y^-1

(I also tried using the -O option to reinstate some gap3 capabilities, but

this apparently does not include Factorization.)

Thanks!

Russell Blyth

=========================================================================== Russell D. Blyth blythrd@slu.edu Associate Professor http://sylow.slu.edu Department of Mathematics and Computer Science Voice: (314)977-2458 Saint Louis University Department: (314)977-2444 221 N. Grand Blvd. Fax: (314)977-3649 St. Louis, MO 63103 Dept: http://euler.slu.edu USA Univ: http://www.slu.edu ===========================================================================

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