Permutation-twisted 5x19 fibre bundles (size 95 = 5 x 19).
These size-95 magmas (~150 submitted by me in June 2026) are the F_5 x F_19 analogue of the size-65 family (see the size-65 page comment) and of the size-35 switched fibre product magma#ed4c392b.
Coordinates (i,u), i in F_5, u in F_19. The 5-class congruence quotient is the F_5 affine magma magma#e549b5f8 (i*j = 2i+4j); the 19-element fibres carry an F_19 affine eq677 law (u*v = 7u+3v, or 7u+4v). 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_19 FIBRE (a bijection of the 19 fibre values, an element of S_19) and (a,b) is one of the F_19 affine laws above.
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_19 it rests on thousands of random permutations all passing, not an exhaustive check. A non-affine p yields a new isomorphism class, so the family is effectively unbounded (150 random permutations gave 150 distinct, all new). Right-cancellative, non-idempotent. Worked example: magma#5bd42664.
[text written by Claude]
dwrensha · 2026-06-17 11:45:41
Permutation-twisted 5x19 fibre bundles (size 95 = 5 x 19).
These size-95 magmas (~150 submitted by me in June 2026) are the F_5 x F_19 analogue of the size-65 family (see the size-65 page comment) and of the size-35 switched fibre product magma#ed4c392b.
Coordinates (i,u), i in F_5, u in F_19. The 5-class congruence quotient is the F_5 affine magma magma#e549b5f8 (i*j = 2i+4j); the 19-element fibres carry an F_19 affine eq677 law (u*v = 7u+3v, or 7u+4v). The operation is
(i,u)*(j,v) = (a u + b v) if i=j (base part 2i+4j)
(i,u)*(j,v) = p^-1(a p(u)+b p(v)) if i!=j
for a fixed but arbitrary permutation p of F_19 and a fibre law (a,b) in {(7,3),(7,4)}.
Every permutation p gives a valid Latin eq677+eq255 magma; generic p yields a new isomorphism class. The family is effectively unbounded (150 random permutations gave 150 distinct, all new). Right-cancellative, non-idempotent. Worked example: magma#5bd42664.
[text written by Claude]
dwrensha · 2026-06-17 12:17:35
dwrensha · 2026-06-17 11:45:41