Equation 677 Database

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Magma b8b29c5f1fff…

magma b8b29c5f1fff
Size
221
Isomorphism class hash
b8b29c5f1fffb38b327224d1460b107a8f6976fec396f3be2bbe4d9cccf78c44
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 22:14:26
Display reorder
220,32,12,52,72,92,117,132,152,162,163,164,165,166,167,161,160,142,2,22,42,62,82,102,122,39,59,79,99,114,139,159,19,127,147,7,27,47,67,87,107,207,202,219,212,34,14,53,73,94,119,134,154,197,198,199,192,193,194,195,196,144,4,24,44,64,84,104,124,35,55,75,95,110,135,155,15,129,149,9,29,48,69,89,109,208,204,218,213,31,11,50,71,91,116,131,150,169,170,171,172,173,174,175,168,140,1,21,40,60,80,100,120,36,56,76,96,111,136,156,16,125,145,6,26,45,65,85,105,205,201,215,211,33,13,54,74,93,118,133,153,183,176,177,178,179,180,181,182,143,3,23,43,63,83,103,123,38,58,78,98,113,138,158,18,128,148,8,28,49,68,88,108,209,203,217,214,30,10,51,70,90,115,130,151,186,187,188,189,190,191,184,185,141,0,20,41,61,81,101,121,37,57,77,97,112,137,157,17,126,146,5,25,46,66,86,106,206,200,216,210 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 = {41} 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 22:14:27 · history