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, 1)); 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).
dwrensha · 2026-04-29 15:53:18