Equation 677 Database

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Magma b9170dc7b819…

magma b9170dc7b819
Size
81
Isomorphism class hash
b9170dc7b819205b58e39f842d5087f493a59482d7b76b80aa3b80f86428ddc9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:22:10
Display reorder
0,1,76,29,42,25,8,35,45,12,80,32,30,64,58,78,44,10,56,21,20,65,15,28,5,62,9,16,19,49,18,41,79,70,77,54,26,53,75,71,52,63,68,13,4,31,47,3,14,60,46,7,22,17,23,67,11,37,2,27,66,40,34,55,73,6,24,33,48,43,72,51,69,39,36,74,57,50,59,61,38 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Linear magma over the extension field F_81 = F_3[α]/⟨α⁴ + α + 2⟩. Operation: x ◇ y = a·x + b·y in F_81 with (a, b) = (2α², 1 + α²). Since α + β = 2α² + 1 + α² = 1 + 3α² = 1 in F_81 (char 3), this is the "Type 1" translation-invariant fully-idempotent linear 677 magma, equivalent to x ◇ y = x + β·(y - x) with β = 1 + α² a primitive 10th root of unity in F_81* (which has order 80, divisible by 10). F_81 is the proper degree-4 extension of F_3; do NOT confuse with the ring Z/81Z (which has zero divisors and is NOT a field). Size 81, fully idempotent, right-cancellative. [text written by Claude]

last edited by dwrensha at 2026-05-16 12:02:52 · history