Equation 677 Database

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Magma ddbd8d97ae3a…

magma ddbd8d97ae3a
Size
221
Isomorphism class hash
ddbd8d97ae3a254f3483d251ad2e862d560673f61f6cdb2eb2b9b2fda0102016
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 22:14:38
Display reorder
220,3,15,193,23,191,4,16,8,192,5,9,17,173,6,10,18,174,7,11,19,12,1,175,20,0,13,176,21,2,14,181,22,25,26,27,29,30,31,24,28,215,210,205,204,105,103,180,126,169,106,127,96,170,107,97,120,189,108,98,121,190,109,99,122,100,110,171,123,111,101,172,124,104,102,168,125,118,119,112,114,115,116,117,113,206,207,216,211,153,151,187,133,188,154,134,144,196,155,145,135,165,156,146,128,166,157,147,129,148,158,167,130,159,149,178,131,152,150,179,132,143,136,137,139,140,141,142,138,209,208,217,212,95,85,161,67,162,88,68,86,177,89,87,69,194,90,80,70,195,91,81,71,82,92,163,64,93,83,164,65,94,84,160,66,77,78,79,73,74,75,76,72,213,219,214,218,60,50,197,32,198,61,33,51,199,62,52,34,182,63,53,35,183,56,54,36,55,57,184,37,58,48,185,38,59,49,186,39,42,43,44,46,47,40,41,45,202,201,203,200 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#add474829cd2325049bfb7e617e6ca8a7671df6e3cee4dda11614250aee3c22d, 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 22:14:39 · history