Equation 677 Database

← all  ·  ← by size  ·  ← size 221

Magma 6be5271db144…

magma 6be5271db144
Size
221
Isomorphism class hash
6be5271db144247b02bf822f9b725c4d21e5a6fbf10140e0c0d9a7996f950798
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 22:14:29
Display reorder
220,77,72,42,47,52,57,62,67,112,117,82,87,90,95,101,107,170,171,172,173,174,175,168,169,150,156,120,125,130,136,142,147,12,17,20,27,32,37,2,7,217,212,202,207,75,70,41,46,51,56,61,65,111,116,80,86,91,96,104,106,179,180,181,182,183,176,177,178,151,155,121,126,131,138,140,146,11,16,21,26,31,36,0,5,215,210,201,206,76,71,40,45,50,55,60,66,110,115,81,85,92,97,100,105,198,199,192,193,194,195,196,197,152,157,122,127,132,135,141,145,10,15,24,25,30,35,1,6,216,211,200,205,78,73,43,48,53,58,63,68,113,118,83,88,93,98,102,108,167,161,160,162,163,164,165,166,153,158,123,128,133,137,143,148,13,18,22,28,33,38,3,8,218,213,203,208,79,74,44,49,54,59,64,69,114,119,84,89,94,99,103,109,190,191,184,185,186,187,188,189,154,159,124,129,134,139,144,149,14,19,23,29,34,39,4,9,219,214,204,209 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#a97cd359209ca8128895583745774fa637e4d6ff9668d716e70c1186faf8de63, 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 22:14:30 · history