Equation 677 Database

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Magma 9ac61f33e0de…

magma 9ac61f33e0de
Size
45
Isomorphism class hash
9ac61f33e0de3061260327cd1f8ec493e58b27cc56b59ca78e22c7e08c8ddabf
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:58:24
Display reorder
40,0,5,7,2,1,3,4,6,41,8,25,33,12,36,17,21,29,42,9,24,32,13,37,16,20,28,44,11,27,34,15,38,19,23,31,43,10,26,35,14,39,18,22,30 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

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.

last edited by dwrensha at 2026-04-29 15:35:16 · history