Equation 677 Database

← all  ·  ← by size  ·  ← size 221

Magma 0ee85980727a…

magma 0ee85980727a
Size
221
Isomorphism class hash
0ee85980727afe5d2369e29f880714b78c04614f988952c5b696662c66b5e513
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 220) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:20:27
Display reorder
220,128,133,138,143,153,57,62,67,72,77,47,12,19,22,27,37,2,7,88,93,103,108,113,118,83,169,170,171,172,173,175,123,148,158,42,52,32,98,174,168,210,208,217,203,127,132,137,142,152,58,63,68,73,78,48,13,17,23,28,38,3,8,87,92,102,107,112,117,82,191,184,185,186,187,189,122,147,157,43,53,33,97,188,190,212,207,218,202,126,131,136,141,151,56,61,66,71,76,46,11,16,21,26,36,0,5,86,91,101,106,111,116,80,197,198,199,192,193,195,120,146,156,40,51,31,96,194,196,211,205,215,200,125,130,135,140,150,55,60,65,70,75,45,10,15,20,25,35,1,6,85,90,100,105,110,115,81,162,163,164,165,166,161,121,145,155,41,50,30,95,167,160,214,206,216,201,129,134,139,144,154,59,64,69,74,79,49,14,18,24,29,39,4,9,89,94,104,109,114,119,84,182,183,176,177,178,180,124,149,159,44,54,34,99,179,181,213,209,219,204 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 221 = 1 + 5*44, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#fec06f1f4e8fb8a75710f5bc1d50e294877f11815b0f1ef2fd4a7890098a78e1, M = {42} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 44): MacNeish's product over GF(4) x GF(11); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-01 22:20:28 · history