Size-49 (= 7²) non-right-cancellative magma with a unique idempotent. Has 8 distinct 7-element sub-magmas, all isomorphic to F_7(4,3), and ALL passing through the unique idempotent — an AG(2,7)-pencil-like configuration. The 49 elements admit a 7-class congruence (an F_7 quotient) where exactly ONE fiber is itself a sub-magma (the fiber containing the idempotent, ≅ F_7(4,3)); the other 7 sub-magmas are transversals, each hitting all 7 fibers in exactly one element. The base operation on the 7 fibers is also iso to F_7. Differs from the AG(2,7)-pencil magma 1b32837d at the same size: both have 8 sub-magmas through the unique idempotent and the same pencil-of-lines combinatorics, but they are NOT isomorphic — they are two inequivalent realizations of an AG(2,7)-pencil structure as a 677 magma.
dwrensha · 2026-04-29 15:49:43