Equation 677 Database

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Magma fc63e2bd6cd9…

magma fc63e2bd6cd9
Size
61
Isomorphism class hash
fc63e2bd6cd94fe49b2d51d39cf1a76badc08b24ac8f870093097593494fa256
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:11
Display reorder
0,1,9,29,58,20,14,27,43,18,13,5,51,22,30,60,59,26,53,11,7,39,34,47,8,46,40,42,49,28,56,54,50,32,33,52,23,48,24,16,55,41,21,3,25,36,45,19,35,17,2,15,44,37,12,38,4,31,57,6,10 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.

last edited by dwrensha at 2026-04-29 23:52:30 · history