Size-45 (= 5 × 9) right-cancellative magma decomposing as a TWISTED fiber bundle: F_5(2,4) base × F_9(3,7) fiber. The 45 elements partition into 5 fibers of 9 elements (an F_5-quotient congruence), and each fiber is itself a sub-magma isomorphic to the F_9 linear magma F_9(3,7). However, unlike the direct product F_5 × F_9, the cross-fiber multiplication is twisted by a non-trivial cocycle — so the magma is NOT isomorphic to the direct product. The database contains 5 iso classes of size 45 sharing this F_5(2,4) base × F_9(3,7) fiber structure: one direct product (57ccc920) and 4 inequivalent non-trivial twists; this magma is one of the 4 twists.
dwrensha · 2026-04-29 15:32:35
Size-45 (= 5 × 9) right-cancellative magma decomposing as a CLEAN fiber bundle: F_5(2,4) base × F_9(3, 7) fiber. The 45 elements partition into 5 fibers of 9 elements (an F_5-quotient congruence), and EVERY fiber is itself a sub-magma isomorphic to F_9(3, 7) (a linear magma over the field F_9 = F_3²). Equivalent to the direct product F_5 × F_9 up to isomorphism.
dwrensha · 2026-04-29 15:35:16
dwrensha · 2026-04-29 15:32:35