Equation 677 Database

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Magma ee53a960fcb4…

magma ee53a960fcb4
Size
121
Isomorphism class hash
ee53a960fcb4822fb3ece18b2952f472cacf55c57f3a61d2020f7406386ce92e
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
dwrensha
Submitted at
2026-04-23 22:00:49
Display reorder
115,2,5,9,8,4,6,3,0,1,7,114,15,19,13,14,16,12,18,10,11,17,120,87,82,89,85,88,84,80,81,86,83,117,56,52,58,59,57,54,50,51,55,53,110,35,37,39,36,30,31,33,32,38,34,119,76,73,74,70,71,78,77,79,72,75,111,23,26,20,21,24,28,25,27,22,29,113,97,98,93,92,90,91,96,94,99,95,118,48,44,40,41,43,45,49,47,46,42,116,65,69,62,63,60,61,68,66,64,67,112,108,104,103,105,102,107,100,101,106,109 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-121 (= 11²) non-right-cancellative magma, all elements idempotent, satisfies eq255. Decomposes as a fiber-bundle-like structure: F_11(10,2) base × F_11(4,8) fiber. The 121 elements partition into 11 fibers of 11 elements (an F_11-quotient congruence), and EVERY fiber is itself an F_11(4,8) sub-magma. In addition, there is exactly one extra 11-element sub-magma — a transversal that hits each fiber in exactly one element — and this transversal is isomorphic to F_11(10,2) (matching the base operation). The 12 size-11 sub-magmas (11 fibers + 1 transversal) form an AG(2,11)-pencil-like configuration. The magma is left-cancellative but not right-cancellative, distinguishing it from the direct product F_11(10,2) × F_11(4,8) (which would be both LC and RC). Each pair of distinct elements is contained in exactly one of the 12 size-11 sub-magmas (covering 660 = 12·C(11,2) of the 7260 = C(121,2) total pairs); pairs across two distinct fibers and not on the transversal lie in no sub-magma.

last edited by dwrensha at 2026-04-29 15:40:00 · history