Equation 677 Database

Magma dd73fb5e7d28…

magma dd73fb5e7d28
Size
49
Isomorphism class hash
dd73fb5e7d2886565f4750055fa04c9c8ec33efabeea12964e33f554e59479cb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
b-reinke
Submitted at
2026-05-26 10:27:33
Display reorder
0,5,2,1,4,41,7,11,6,9,8,37,10,18,20,22,21,39,19,23,38,17,13,16,12,14,15,30,31,32,33,35,36,34,26,24,28,29,25,27,40,48,47,44,45,42,46,43,3 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,3) and 1 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]

last edited by dwrensha at 2026-05-27 05:14:59 · history