Equation 677 Database

Size-55 Latin eq677 magma: a permutation-twisted 5x11 fibre bundle. See the size-55 page comment for the general family. There is a 5-class congruence theta with five 11-element classes. Coordinates (i,u): i in F_5 is the class index, u in F_11 is the fibre coordinate; each row Ci lists the elements with u=0,1,...,10: C0: 5,53,41,49,12,16,20,28,45,24,37 C1: 6,38,46,34,17,21,25,13,50,9,42 C2: 8,48,36,44,27,11,15,23,40,19,52 C3: 7,43,51,39,22,26,10,18,35,14,47 C4: 54,32,1,29,30,33,3,0,4,31,2 The quotient M/theta is magma#e549b5f8, the F_5 affine law i*j = 2i+4j. Every theta-class is a copy of magma#ca58a4a9, the F_11 affine law u*v = 4u+8v. In these coordinates: (i,u)*(j,v) = (2i+4j, 4u+8v) if i=j (i,u)*(j,v) = (2i+4j, p^-1(4 p(u)+8 p(v))) if i!=j with off-diagonal twist permutation p = (8,9,1,2,5,3,7,4,0,10,6), i.e. p(0)=8, p(1)=9, ..., p(10)=6. Right-cancellative, non-idempotent. [text written by Claude]