Equation 677 Database

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Magma 57ccc920f3a4…

magma 57ccc920f3a4
Size
45
Isomorphism class hash
57ccc920f3a4ae4bbffe4b3ea9285a0b0b067889bdceee076361c43900c3431e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:58:24
Display reorder
40,3,19,15,20,11,28,24,7,41,0,16,12,22,8,30,26,4,42,1,17,13,21,9,29,25,5,44,33,36,35,37,39,32,38,34,43,2,18,14,23,10,31,27,6 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-45 (= 5 × 9) magma: the direct product F_5(2,4) × F_9(3,7). The 45 elements partition into 5 fibers of 9, every fiber is an F_9(3,7) sub-magma, and the cross-fiber multiplication is the trivial (direct-product) cocycle. F_9 is the field of order 9 = 3², and (3,7) gives one of the two F_9-linear magmas satisfying equation 677. The database has 4 other size-45 magmas (9ac61f33, 05aba89c, a97cd359, fec06f1f) with the same F_5 base × F_9 fiber structure but non-trivial twists.

last edited by dwrensha at 2026-04-29 15:35:17 · history