Equation 677 Database

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Magma 1913ccf6cc0f…

magma 1913ccf6cc0f
Size
221
Isomorphism class hash
1913ccf6cc0f197c120e2bbb4d48fec4612fae83663111c8a11fb0293e11d3fd
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 22:02:58
Display reorder
220,148,132,154,194,149,133,155,195,150,134,156,160,151,135,157,161,144,128,158,162,163,129,145,159,180,130,146,152,179,131,147,153,137,138,139,141,142,143,136,140,212,215,213,214,62,46,48,177,63,47,49,178,56,40,50,197,57,41,51,191,58,42,52,192,193,43,59,53,175,44,60,54,176,45,61,55,39,32,33,35,36,37,38,34,219,217,216,218,67,89,73,174,68,90,74,196,69,91,75,168,70,92,76,169,71,93,77,170,171,94,64,78,172,95,65,79,173,88,66,72,82,83,84,86,87,80,81,85,207,205,206,204,119,103,125,166,112,96,126,164,113,97,127,187,114,98,120,188,115,99,121,189,190,100,116,122,167,101,117,123,165,102,118,124,108,109,110,104,105,106,107,111,208,211,209,210,16,1,30,198,17,0,31,199,18,2,24,181,19,3,25,182,20,4,26,183,184,5,21,27,185,6,22,28,186,7,23,29,13,14,15,9,10,11,12,8,201,203,200,202 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#57ccc920f3a4ae4bbffe4b3ea9285a0b0b067889bdceee076361c43900c3431e, 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 22:02:59 · history