Equation 677 Database

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Magma f99ffe386adf…

magma f99ffe386adf
Size
221
Isomorphism class hash
f99ffe386adf93a16ee7886ac0f3f0add079caf01dfc6a332006987af59f9056
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 22:14:49
Display reorder
220,63,90,209,186,153,157,60,69,88,71,208,216,214,215,91,211,67,210,158,184,160,152,62,187,61,154,70,155,66,162,65,159,68,64,89,185,156,213,219,212,161,217,163,218,8,77,203,170,127,130,37,17,79,27,200,183,151,112,78,207,42,194,104,176,119,133,25,178,30,122,1,106,5,94,33,138,22,47,76,180,142,14,206,57,114,2,124,99,41,74,193,177,140,110,52,36,73,16,197,167,116,118,75,188,59,201,150,173,113,146,45,164,44,97,38,137,56,134,12,98,15,54,72,169,148,21,191,24,103,50,95,126,0,85,189,174,101,131,26,53,87,46,195,172,120,92,86,202,9,198,125,171,143,123,18,179,3,115,11,93,28,109,34,107,48,6,84,165,102,58,196,23,147,31,141,128,4,83,190,175,136,111,43,51,81,35,192,182,96,105,80,204,39,199,149,168,129,139,49,181,40,144,29,100,55,121,13,135,32,10,82,166,108,7,205,19,145,20,132,117 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 = {0} 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 22:14:49 · history