Equation 677 Database

← all  ·  ← by size  ·  ← size 221

Magma 92c2e53488b8…

magma 92c2e53488b8
Size
221
Isomorphism class hash
92c2e53488b8eed7e96060b0fef96d29843bbd4dfd8b88f06390d4558221f997
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 22:03:01
Display reorder
220,30,18,193,10,11,31,19,196,24,12,20,171,25,13,21,172,26,14,22,173,23,15,27,179,16,8,28,169,9,17,29,170,5,6,7,0,2,3,4,1,206,216,205,200,126,114,167,106,107,127,115,168,120,108,116,195,121,109,117,191,122,110,118,192,119,111,123,164,112,104,124,165,105,113,125,166,101,102,103,97,98,99,100,96,207,208,217,209,137,144,194,147,148,139,146,197,141,150,149,174,143,152,151,175,128,154,153,176,155,156,131,177,157,158,133,181,145,159,135,180,136,138,140,129,130,132,134,142,210,213,211,212,94,82,178,74,75,95,83,163,88,76,84,189,89,77,85,190,90,78,86,188,87,79,91,161,80,72,92,162,73,81,93,160,69,70,71,65,66,67,68,64,214,218,215,219,61,49,198,41,42,62,50,199,63,43,51,182,56,44,52,183,57,45,53,184,54,46,58,185,55,47,59,186,40,48,60,187,36,37,38,32,33,34,35,39,204,202,203,201 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#582a66580be0451838f983f6a718458e80606e181d12a16f31ef8f68f49e9e84, 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 22:03:02 · history