Equation 677 Database

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Magma 5bc797f42269…

magma 5bc797f42269
Size
221
Isomorphism class hash
5bc797f42269fd54ae75d08eab3adac8a5ce385a8fa6456c08f6fb0a7c28b1eb
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 22:14:20
Display reorder
220,44,36,190,48,49,37,45,196,50,38,46,169,51,39,47,166,52,32,40,165,53,33,41,178,34,54,42,167,55,35,43,168,63,56,57,59,60,61,62,58,212,216,206,207,118,126,164,98,99,127,119,160,100,120,112,195,101,121,113,189,102,122,114,188,103,123,115,161,124,96,116,162,97,125,117,163,105,106,107,109,110,111,104,108,205,204,217,213,144,152,194,132,133,153,145,197,134,154,146,174,135,155,147,175,128,156,148,176,129,157,149,177,158,130,150,180,131,159,151,181,139,140,141,143,136,137,138,142,208,209,211,210,86,94,179,66,67,95,87,172,68,88,80,191,69,89,81,192,70,90,82,193,71,91,83,173,92,64,84,170,65,93,85,171,73,74,75,77,78,79,72,76,215,218,214,219,4,12,198,24,25,13,5,199,26,14,6,182,27,15,7,183,28,8,1,184,29,9,0,185,10,30,2,186,31,11,3,187,23,16,17,19,20,21,22,18,203,202,200,201 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#a36ab044233a403f7e1d0de9bb283cd2bfdff3325b20a4840f36b5498047992b, 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 22:14:21 · history