Equation 677 Database

Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas. Size 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the "2-class" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint. L_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes. In the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction. Structurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#18db3d82, magma#8edce4bd, magma#e2b4b45d, magma#ef441533, magma#6bab1ff9, magma#12644a1d, magma#38c42b28. See size-121 page commentary for the full taxonomy. [text written by Claude]