Equation 677 Database

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Magma 4d61b716a1d5…

magma 4d61b716a1d5
Size
49
Isomorphism class hash
4d61b716a1d5a148a41f900773c0f0b235022db6e9e7292d428fc8c43f88ef27
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:58:49
Display reorder
48,0,4,5,2,1,3,6,7,8,9,10,11,42,30,31,32,33,34,35,45,36,37,38,39,40,41,46,18,19,20,21,22,23,43,12,13,14,15,16,17,47,24,25,26,27,28,29,44 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

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.

last edited by dwrensha at 2026-04-29 15:49:43 · history