Equation 677 Database

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Magma 903681efcb44…

magma 903681efcb44
Size
221
Isomorphism class hash
903681efcb449f8f4588986d6b55fe24ce2b54e89877916d0e77780392e8cfb7
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 21:46:22
Display reorder
220,195,66,92,73,67,187,93,74,68,188,94,75,69,174,95,76,70,170,88,77,71,171,89,78,64,172,90,79,65,173,91,72,83,84,85,87,80,81,82,86,206,211,219,215,163,156,137,145,157,164,138,146,158,160,139,147,159,185,140,148,152,192,141,149,153,191,142,150,154,161,143,151,155,162,136,144,128,129,130,132,133,134,135,131,204,209,218,214,193,38,56,45,39,186,57,46,32,194,58,47,33,165,59,40,34,166,60,41,35,167,61,42,36,168,62,43,37,169,63,44,55,48,49,51,52,53,54,50,217,212,208,207,177,110,118,99,111,178,119,100,104,179,112,101,105,189,113,102,106,190,114,103,107,196,115,96,108,175,116,97,109,176,117,98,127,120,121,123,124,125,126,122,210,205,213,216,199,24,13,21,25,197,14,22,26,198,15,23,27,180,8,16,28,181,9,17,29,182,10,18,30,183,11,19,31,184,12,20,4,5,6,1,0,2,3,7,200,201,202,203 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#0d12ed9a51cc47cc6a9252d10a47bf06cd83adb396451e6398bb0fe7149e0b14, 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 21:46:23 · history