Equation 677 Database

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Magma 0b5942e586fb…

magma 0b5942e586fb
Size
83
Isomorphism class hash
0b5942e586fb32c27f22fa162ea5918ad21b2a1c0e77f6b218411c030d16b62b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:24:09
Display reorder
0,1,82,25,70,28,49,20,62,52,43,7,12,2,63,27,8,31,73,9,22,55,21,66,34,71,32,36,48,41,42,53,40,23,37,24,72,57,17,65,10,47,60,19,16,50,74,3,51,78,14,77,69,4,58,45,26,35,11,79,76,54,68,44,64,29,59,15,6,75,56,61,38,30,81,46,5,80,13,67,18,33,39 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-83 sporadic magma. Prime size, but no F_83-linear magma satisfies equation 677 — the diophantine system "ab(b²+1) ≡ 1 (mod 83) and a + a²b² + b³ ≡ 0 (mod 83)" has no solution. So this is a non-linear 677 magma at prime size, like the size-29 magma 9f34fd7d. It is a quasigroup (LC + RC), all 83 elements are idempotent, and it has NO non-trivial sub-magmas (every pair of distinct elements generates the whole magma). Both L_x and R_x are permutations with uniform cycle types across all x: L_x = (82 + 1) — one 82-cycle and the fixed point at x — and R_x = (41 + 41 + 1) — two 41-cycles plus the fixed point at x. The L vs R asymmetry distinguishes this from the size-29 sporadic magma, which has matching L_x and R_x types (14 + 14 + 1). This is the only size-83 magma in the database.

last edited by dwrensha at 2026-04-29 17:04:55 · history