Equation 677 Database

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Magma 0f61935b4db3…

magma 0f61935b4db3
Size
49
Isomorphism class hash
0f61935b4db30f484ad547e361777e867ee1b016fc2a1a79c60017913a4e9023
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:58:41
Display reorder
48,42,47,43,45,44,46,0,1,36,4,3,5,2,12,16,13,15,38,14,17,6,9,11,7,8,10,37,24,40,28,26,25,29,27,30,35,32,41,33,31,34,18,20,21,22,23,39,19 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-49 (= 7²) right-cancellative magma. Has 8 distinct 7-element sub-magmas, all passing through the unique idempotent — an AG(2,7)-pencil-like configuration. The 49 elements admit a 7-class congruence (F_7 quotient with base ≅ F_7(4, 1)) where exactly ONE fiber is itself a sub-magma (the fiber containing the idempotent, ≅ F_7(4, 3)); the other 7 sub-magmas through the idempotent are transversals, each hitting all 7 fibers in exactly one element. The 8 sub-magmas correspond to the 8 lines through the origin in AG(2,7).

last edited by dwrensha at 2026-04-29 15:53:17 · history