Equation 677 Database

← all  ·  ← by size  ·  ← size 49

Magma 3d9ea61f4ac8…

magma 3d9ea61f4ac8
Size
49
Isomorphism class hash
3d9ea61f4ac8ad5b1b47ed51fe6742da3b2f6d6bdf7a08716863169482908deb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:58:26
Display reorder
48,0,33,5,3,31,18,34,15,40,29,7,41,38,4,20,28,11,10,8,46,1,26,14,43,19,35,25,47,23,37,21,45,16,24,2,44,6,12,13,30,22,32,36,39,9,27,42,17 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Linear magma over the extension field F_49 = F_7[α]/⟨α² - 3⟩. Operation: x ◇ y = a·x + b·y in F_49 with (a, b) = (2, 1 + α). Here β = 1 + α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_49, and α_coef = -β³ - β - 1 = 2 (in F_49). This is Pace Nielsen's Type-2 non-fully-idempotent linear 677 magma family. F_49 is the proper degree-2 extension of F_7; do NOT confuse with the ring Z/49Z (which has zero divisors and is NOT a field). Note that the size-49 family in the DB includes two distinct constructions: this one (over F_49) and others (magma#bd9c4bf0, magma#a9267aad) over the ring Z/49Z. Size 49, not fully idempotent, right-cancellative. [text written by Claude]

last edited by dwrensha at 2026-05-16 12:02:52 · history