Equation 677 Database

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Magma fe0d361843fd…

magma fe0d361843fd
Size
89
Isomorphism class hash
fe0d361843fd58d79eadcbfa1b4a4ca74dd9fca22f67cd7d941af3e9cfc634d5
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 78 (nullity 11) what is this?
Submitted by
omegaestable
Submitted at
2026-09-30 17:58:33
Display reorder
88,80,86,83,82,85,87,81,84,76,21,6,31,16,1,26,11,63,48,73,58,43,68,53,38,75,20,5,30,15,4,25,10,78,23,8,33,18,2,28,13,79,24,9,34,19,3,29,14,61,46,71,56,40,66,51,36,60,45,70,55,41,65,50,35,64,49,74,59,44,69,54,39,77,22,7,32,17,0,27,12,62,47,72,57,42,67,52,37 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-89 non-right-cancellative Eq677 magma with right identity e. Carrier: {e} ∪ (Z/11Z × Z/8Z). Each set {e} ∪ ({i} × Z/8Z) is a copy of F_9, with e identified with 0 and operation u ◇ v = u + βv, where F_9 = F_3[α]/(α² + 1) and β = 2 + α. For distinct base labels i,j, define (i,s) ◇ (j,t) = (6i + 6j, t) if j−i ∈ {1,3,4,5,9} mod 11, and (6i + 6j, −s−t) otherwise; first coordinates are mod 11 and second coordinates mod 8. The rows are permutations, but columns are not: in the supplied table labeling, 1 ◇ 9 = 2 ◇ 9 = 49. Thus this is a right-unital left quasigroup that is not a quasigroup. The magma is nonmedial and satisfies E255. Exhaustive replay checks all 7,921 E677 instances and all 89 E255 instances.

last edited by omegaestable at 2026-09-30 18:21:35 · history