Equation 677 Database

← all  ·  ← by size  ·  ← size 80

Magma afeae577d228…

magma afeae577d228
Size
80
Isomorphism class hash
afeae577d2282082c9a37ff1c658983483099e1335de87d821c98b8bb04da69f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:22:08
Display reorder
0,20,56,40,32,48,60,52,64,28,24,76,72,68,44,36,1,21,53,41,73,45,77,61,65,29,57,25,49,37,33,69,3,19,55,31,75,59,63,23,27,47,51,67,39,71,43,35,2,22,74,58,66,34,50,30,38,54,70,62,26,78,42,46,4,5,10,18,7,9,17,13,79,16,12,15,8,14,11,6 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-80 (= 5 × 16) right-cancellative magma, with EVERY element idempotent. Decomposes as a TWISTED fiber bundle: F_5(2,4) base × F_16(9,8) fiber. The 80 elements partition into 5 fibers of 16 (an F_5-quotient congruence), and every fiber is itself a closed sub-magma isomorphic to F_16(9,8) (a linear magma over the extension field F_16 = F_2⁴). However, the cross-fiber multiplication has a non-trivial cocycle, so the magma is NOT isomorphic to the direct product F_5 × F_16. The all-idempotence comes from both factors being all-idempotent: F_5(2,4) has 2+4=6≡1 (mod 5) and F_16(9,8) has 9+8=1 (in F_16, where addition is XOR), so x ◇ x = (a+b)·x = x in each. Quasigroup (LC + RC). Compare with the size-80 twist 0998765e, which uses F_16(6,11) instead of F_16(9,8) as fiber: F_16(6,11) is NOT all-idempotent (6 XOR 11 = 13 in F_16), so 0998765e has only 5 idempotents (one per fiber), not all 80.

last edited by dwrensha at 2026-04-29 16:52:53 · history