Equation 677 Database

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Magma cef8c754b9ab…

magma cef8c754b9ab
Size
221
Isomorphism class hash
cef8c754b9abd894894abc7fec7d65235aa9b5df7303e81e1707cb1d90494db6
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 166 (nullity 55) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:20:18
Display reorder
220,0,143,38,141,107,101,145,117,98,4,94,127,54,22,42,85,48,147,112,103,87,86,84,34,132,139,130,12,189,182,165,164,170,167,191,29,25,9,46,188,43,51,207,194,60,218,64,156,159,161,155,214,160,68,152,215,212,213,217,91,71,163,154,162,89,88,90,66,153,158,157,62,209,184,185,186,216,187,211,61,65,67,63,210,70,69,208,219,7,140,41,142,129,110,97,92,116,45,105,131,33,26,37,83,21,126,121,150,81,80,82,32,135,137,124,17,201,180,176,168,179,183,200,28,53,24,3,192,57,11,205,204,2,100,40,115,113,144,119,104,109,10,96,136,6,31,5,74,18,123,146,122,73,75,72,56,134,111,148,50,195,178,171,173,169,175,199,27,52,36,15,197,59,44,203,193,1,125,39,93,102,114,99,108,118,14,95,128,49,23,20,76,55,149,138,106,78,77,79,16,133,120,151,35,198,177,174,181,172,166,190,30,58,47,19,206,8,13,202,196 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#f2ff036103ce87dd22beb1b750344314c69ce6fbd5e0a995701630860538525a, M = {28} 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 22:20:19 · history