Equation 677 Database

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Magma 04ee6361223e…

magma 04ee6361223e
Size
221
Isomorphism class hash
04ee6361223e08c9dc38307a858892a1e05aa3eb627258594179750397a8e7ef
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 22:14:41
Display reorder
220,67,189,76,59,68,187,77,60,69,188,78,61,70,163,79,62,71,164,72,63,64,165,73,56,65,166,74,57,66,167,75,58,87,80,81,83,84,85,86,82,212,218,216,215,118,171,96,110,119,172,97,111,112,173,98,104,113,192,99,105,114,195,100,106,115,196,101,107,116,174,102,108,117,175,103,109,93,94,95,89,90,91,92,88,205,204,206,207,141,190,122,148,142,191,123,150,143,194,124,152,136,168,125,154,137,169,126,156,138,170,127,158,139,179,120,145,140,178,121,146,133,134,135,129,130,131,132,128,208,209,211,210,157,177,13,3,159,160,14,4,144,176,15,5,147,186,8,6,149,185,9,7,151,193,10,1,153,161,11,0,155,162,12,2,16,17,18,20,21,22,23,19,214,217,213,219,25,197,51,37,26,198,52,38,27,199,53,39,28,180,54,32,29,181,55,33,30,182,48,34,31,183,49,35,24,184,50,36,40,41,42,44,45,46,47,43,201,200,203,202 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#b9b27d62068a99bbcb46ebf2d3f4c6e589d66bca98ce6da281f596d3430349d1, 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 22:14:42 · history