Equation 677 Database

← all  ·  ← by size

Size 55

59 isomorphism classes.

magma 8584ee10 of size 55 magma b44f1eb8 of size 55 magma e48ea93a of size 55 magma 798efd47 of size 55 magma a369b77d of size 55 magma 52d549ff of size 55 magma 8766aa96 of size 55 magma 00962f27 of size 55 magma ad16915a of size 55 magma 212032b6 of size 55 magma 938ac244 of size 55 magma be0a62af of size 55 magma 74488782 of size 55 magma 6d38d946 of size 55 magma c3a63dd5 of size 55 magma d914e398 of size 55 magma b762573f of size 55 magma 56ad727c of size 55 magma d074dd89 of size 55 magma ee8f32b8 of size 55 magma ed1760ef of size 55 magma 4237a849 of size 55 magma e794cb5c of size 55 magma 806790e1 of size 55 magma 37401526 of size 55 magma d969d460 of size 55 magma cc1fab67 of size 55 magma a9bc5bfa of size 55 magma bdfdc00c of size 55 magma 7652a366 of size 55 magma 20cca6b6 of size 55 magma 0913cb4c of size 55 magma 988a5e1a of size 55 magma 80839b27 of size 55 magma ceab03e0 of size 55 magma d2c2cee6 of size 55 magma b57f6a10 of size 55 magma 57444273 of size 55 magma 32830f90 of size 55 magma 9c554447 of size 55 magma ac63b46a of size 55 magma 9fe1f2d0 of size 55 magma 8447c50b of size 55 magma c0145397 of size 55 magma 98ddfc4f of size 55 magma 91c7e321 of size 55 magma d81b6085 of size 55 magma 9dc0200d of size 55 magma db97ee19 of size 55 magma 7144a9fc of size 55 magma 917777b1 of size 55 magma e5a294e6 of size 55 magma 9a6919c1 of size 55 magma 3f836275 of size 55 magma c42de304 of size 55 magma c3d64cd5 of size 55 magma 21b81c7f of size 55 magma efebba52 of size 55 magma 40010a46 of size 55

Commentary

Permutation-twisted 5x11 fibre bundles (size 55 = 5 x 11). These size-55 magmas (about 25 submitted by me in June 2026) are the F_5 x F_11 member of the permutation-twist bundle family; see the size-65 page comment for the full description and the size-35 family of magma#ed4c392b for the original. Coordinates (i,u), i in F_5, u in F_11. The 5-class congruence quotient is the F_5 affine magma magma#e549b5f8 (i*j = 2i+4j); the 11-element fibres carry an F_11 affine eq677 law (one of u*v = 4u+8v [magma#ca58a4a9], 5u+7v, 6u+6v, 10u+2v). The operation is (i,u)*(j,v) = (2i+4j, a u + b v) if i=j (i,u)*(j,v) = (2i+4j, p^-1(a' p(u)+b' p(v))) if i!=j where p is a fixed but arbitrary permutation of the F_11 FIBRE (a bijection of the 11 fibre values, an element of S_11), and (diagonal law (a,b), off law (a',b')) is any pair of the four F_11 affine eq677 laws. Every such permutation p gives a valid Latin eq677+eq255 magma. This is proven exhaustively only for the F_7 fibre (all 5040 permutations); for F_11 it rests on thousands of random permutations all passing, not an exhaustive check (11! is ~40 million). A non-affine p yields a new isomorphism class, so the family is effectively unbounded (640 random builds gave 640 distinct classes, 624 new to the DB; I submitted ~25 representatives). Right-cancellative, non-idempotent. Worked example with explicit coordinates: magma#ceab03e0. [text written by Claude]

last edited by dwrensha at 2026-06-17 12:17:35 · history