Equation 677 Database

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Magma 5bf267d034ff…

magma 5bf267d034ff
Size
221
Isomorphism class hash
5bf267d034ff4d45b4358de4604a46a59c5e506f53a3e36b69908f472f4a1949
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 22:14:23
Display reorder
220,53,48,58,63,68,73,78,43,130,135,140,145,150,155,121,126,116,82,85,91,96,100,106,111,33,38,3,8,13,17,23,28,198,199,192,193,194,195,196,197,201,207,218,212,51,45,56,61,66,71,76,40,132,137,142,147,152,157,122,127,118,81,86,90,95,101,105,110,31,36,0,6,11,19,21,26,176,177,178,179,180,181,182,183,202,206,217,211,52,47,57,62,67,72,77,42,133,138,143,148,153,158,123,128,117,83,88,93,98,103,108,113,32,37,2,7,10,16,22,27,175,168,169,170,171,172,173,174,203,208,215,210,54,49,59,64,69,74,79,44,134,139,144,149,154,159,124,129,119,84,89,94,99,104,109,114,34,39,4,9,14,18,24,29,167,161,160,162,163,164,165,166,204,209,219,213,50,46,55,60,65,70,75,41,131,136,141,146,151,156,120,125,115,80,87,92,97,102,107,112,30,35,1,5,12,15,20,25,189,190,191,184,185,186,187,188,200,205,216,214 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 = {40} 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 22:14:24 · history