File: 11gp-3-Engel-Id

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#Example: "11gp-3-Engel-Id" . . . 3-Engel group for prime 11
#Non-trivial example of using the `Identities' option
#vars: F, a, b, G, f, procId, Q;
#options: 
F := FreeGroup("a", "b"); a := F.1; b := F.2;
G := F/[ a^11, b^11 ];
## All word pairs u, v in the pc generators of the 11-quotient Q of G 
## must satisfy the Engel identity: [u, v, v, v] = 1.
f := function(u, v) return PqLeftNormComm( [u, v, v, v] ); end;
#alt: do
#procId := PqStart( G );
#alt: sub <procId> for <G>
Q := Pq( G : Prime := 11, Identities := [ f ] );
## We do a ``sample'' check that pairs of elements of Q do satisfy
## the given identity:
f( Random(Q), Random(Q) );
f( Q.1, Q.2 );