Equation 677 Database

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Magma da462aa1ec01…

magma da462aa1ec01
Size
125
Isomorphism class hash
da462aa1ec01d881728510c7847ab9bee106493c1131d69f26252693262d499f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-06-10 14:17:16
Display reorder
60,64,77,71,74,1,12,4,16,8,96,92,88,81,85,28,32,36,20,24,48,56,44,52,40,0,17,13,9,5,49,53,57,41,45,97,82,93,86,89,61,68,65,75,78,29,21,33,25,37,39,27,35,23,31,67,70,63,76,73,84,91,80,95,99,43,59,55,51,47,19,3,7,11,15,54,46,58,50,42,30,26,22,38,34,90,94,98,87,83,10,18,6,14,2,66,62,72,69,79,109,113,117,121,105,116,104,112,120,108,100,103,124,101,102,118,110,122,114,106,115,111,107,123,119 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

x \diamond y = x^2 * y^-1 in SmallGroup(125,3) (the group of strictly upper triangular 3x3 matrices in F_5), as constructed in https://leanprover.zulipchat.com/#narrow/channel/458659-Equational/topic/FINITE.3A.20677.20-.3E.20255/near/490276270 Display order: elements are indexed 25a+5b+c via the normal form x = g1^a g2^b z^c, where g1, g2 generate the group and z = [g1,g2] generates the center. In these coordinates the operation is (a,b,c) \diamond (a',b',c') = (2a-a', 2b-b', 2c-c'-ab-a'b'+2a'b), so the table is the self-similar "2x-y mod 5" pattern at two nested scales (the 25x25 superblocks in a, the 5x5 blocks in b), with the central coordinate contributing the affine fine structure. [text written by Claude]

last edited by dwrensha at 2026-06-12 17:15:50 · history