Equation 677 Database

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Magma b4b411fb53aa…

magma b4b411fb53aa
Size
221
Isomorphism class hash
b4b411fb53aae833a42cb1490a6d3c823c533f5ece3c630cb62b61e1ce5346f9
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: yes · normal: yes · rank: 166 (nullity 55) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:02:48
Display reorder
211,125,66,121,13,0,175,75,34,71,51,46,141,150,65,145,85,111,138,146,61,2,90,78,11,12,134,158,42,40,95,80,154,105,94,24,106,57,168,130,160,30,159,16,120,176,212,213,182,197,181,206,216,207,214,219,201,195,194,192,189,190,196,191,193,180,205,200,188,199,210,217,209,183,198,184,202,203,215,179,220,178,187,208,185,204,177,186,218,157,133,101,10,7,170,153,83,97,39,41,25,115,123,69,124,45,50,70,36,6,76,84,19,3,149,140,89,53,60,148,137,110,93,56,109,166,169,119,136,165,33,23,129,144,63,64,20,21,171,139,113,88,87,55,132,82,100,96,99,38,77,44,104,22,152,114,5,14,35,68,74,127,167,48,27,49,59,163,108,32,172,164,28,128,118,8,135,117,162,107,17,15,174,161,92,29,31,58,103,37,102,155,43,98,81,156,79,9,131,91,18,4,54,112,151,62,86,142,147,143,47,73,122,52,173,67,72,26,126,1,116 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#367f17fc60a59c9bc0da7ab80ab9790f20864b313a87bbac2b01a38063217608, M = {1} 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: 221.

last edited by qawbecrdtey at 2026-10-01 22:02:49 · history