Equation 677 Database

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Magma 2884a58dd605…

magma 2884a58dd605
Size
221
Isomorphism class hash
2884a58dd6059de9ecd382c9cad231df750cd3cc56d6f9a47ba2f8e9ca5b2a56
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 22:15:04
Display reorder
220,55,146,48,38,77,78,112,192,203,5,149,107,109,124,76,23,100,129,3,189,0,42,198,196,148,26,10,15,18,52,172,87,179,45,59,115,93,144,135,168,141,102,165,174,32,95,27,19,82,79,122,200,205,50,131,151,137,113,81,13,104,101,6,191,8,40,190,202,145,4,36,30,57,47,178,80,181,53,21,96,94,99,119,176,106,123,167,166,69,162,70,67,88,89,156,209,211,62,161,155,157,160,91,68,214,215,212,208,66,60,210,219,218,213,65,61,63,217,216,90,187,71,64,153,158,163,159,185,152,154,184,186,16,142,43,34,86,83,132,204,193,46,116,150,139,105,85,7,110,103,12,197,14,24,207,188,98,22,39,49,56,2,164,84,169,31,29,147,114,128,126,180,125,118,173,183,9,140,41,11,74,75,120,195,194,37,108,143,133,92,72,1,127,134,25,206,35,58,199,201,130,33,51,17,44,28,177,73,170,54,20,117,136,121,111,171,97,138,182,175 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 = {4} 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 22:15:05 · history