Equation 677 Database

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Magma ec3a53e83266…

magma ec3a53e83266
Size
221
Isomorphism class hash
ec3a53e8326602a5130c51df4f3a7189fddcbe88406122e157c14a9272bc113c
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 22:02:55
Display reorder
220,100,187,121,105,101,188,122,106,102,189,123,107,103,165,124,108,96,166,125,109,167,97,126,110,168,98,127,111,169,99,120,104,117,118,119,113,114,115,116,112,217,218,219,216,158,162,142,149,159,163,143,150,152,164,136,151,153,186,137,144,154,195,138,145,185,155,139,146,160,156,140,147,161,157,141,148,130,131,132,134,135,128,129,133,209,210,208,211,21,194,4,26,22,193,5,27,23,196,6,28,16,173,7,29,17,174,1,30,175,18,0,31,176,19,2,24,177,20,3,25,8,9,10,12,13,14,15,11,212,215,213,214,62,179,46,53,63,170,47,54,56,178,40,55,57,190,41,48,58,191,42,49,192,59,43,50,171,60,44,51,172,61,45,52,34,35,36,38,39,32,33,37,200,202,201,203,73,197,87,64,74,198,80,65,75,199,81,66,76,180,82,67,77,181,83,68,182,78,84,69,183,79,85,70,184,72,86,71,91,92,93,95,88,89,90,94,206,204,207,205 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#4da2b2632ba160a3bb7e62025fcd109d3278e3e2e804b512832b5be73a527984, 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 22:02:56 · history