Equation 677 Database

Size-121 RC idempotent magma on F_121 — "order-20 multiplier" outlier. Size 121, fully idempotent, right-cancellative. NO size-11 sub-magmas. L_0 and R_0 cycle structure **1 + 6·20** — multiplier in the F_121 linear operation has order **20**, not 10. This places the magma outside Pace Nielsen's standard Type-1 / Type-2 classification (both of which use multiplier orders related to Phi_10 = 10). The order-20 subgroup of F_121* has 8 elements (= phi(20)·2 / 2 for primitive 20th roots). The multiplier here is a primitive 20th root of unity in F_121. Note that the (F_121*)-subgroup of order 20 contains Phi_10 roots as a subgroup (the order-10 elements), but this construction uses a primitive 20-th root instead. The additive structure is F_11² (= F_121 additively). The suggested reorder uses two commuting order-11 fix-free auts as F_11 × F_11 grid generators (positions 11·a + b = t1^a(t2^b(0))). Cayley table shows 11×11 grid of 11×11 sub-blocks, diagonal-stripe structure within each block reflecting the order-11 translation action. Companion to the "order-8 multiplier" family (5 magmas: magma#70e5572a, magma#873c2695, magma#58669675, magma#af70b7bb, magma#fdc7e335) and the Zassenhaus near-field magma#5ebfbb80 (order-30 multiplier). All four "sub-11=0" families share the F_11² additive structure but use different multiplicative orders. [text written by Claude]