Equation 677 Database

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Magma 42ef18692fee…

magma 42ef18692fee
Size
221
Isomorphism class hash
42ef18692feead4a7e06a42e740be739a21845a9749c3d809c0e6f42708ec02f
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 22:20:21
Display reorder
220,120,126,131,136,146,165,166,167,161,160,163,75,41,45,50,60,65,70,19,23,33,38,3,8,13,85,90,95,100,105,116,156,141,151,162,164,55,28,111,80,211,205,216,200,122,127,132,137,147,190,191,184,185,186,188,77,42,47,52,62,67,72,15,20,30,35,1,5,12,87,92,97,102,107,117,157,142,152,187,189,57,25,112,82,213,207,217,202,123,128,133,138,148,169,170,171,172,173,175,78,43,48,53,63,68,73,18,22,32,37,2,7,10,88,93,98,103,108,118,158,143,153,174,168,58,27,113,83,210,208,218,203,121,125,130,135,145,193,194,195,196,197,199,76,40,46,51,61,66,71,16,21,31,36,0,6,11,86,91,96,101,106,115,155,140,150,198,192,56,26,110,81,214,206,215,201,124,129,134,139,149,178,179,180,181,182,176,79,44,49,54,64,69,74,17,24,34,39,4,9,14,89,94,99,104,109,119,159,144,154,183,177,59,29,114,84,212,209,219,204 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#fec06f1f4e8fb8a75710f5bc1d50e294877f11815b0f1ef2fd4a7890098a78e1, 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 22:20:22 · history