Equation 677 Database

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Magma 09a525dc5c40…

magma 09a525dc5c40
Size
61
Isomorphism class hash
09a525dc5c4006d1a4ad789b4f20de96b39a0407c55b521ebc9dc0f67a28f199
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:48
Display reorder
0,1,10,26,15,51,38,55,13,32,31,21,50,14,39,46,56,41,4,34,49,35,33,40,9,16,30,12,2,52,29,17,25,23,42,28,45,58,27,5,11,43,18,37,8,53,44,59,47,60,57,6,7,20,54,48,24,19,22,3,36 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) (the unique F_5 linear satisfying eq677). 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). Not isomorphic to any F_61-linear magma — those are 82a4911c, d5df0d93, e70931b6, f2d8c865. Same family as the existing Steiner S(2,5,61) magma 03138da9 in the database.

last edited by dwrensha at 2026-04-29 23:52:19 · history