Equation 677 Database

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Magma e87c4acc4d1b…

magma e87c4acc4d1b
Size
221
Isomorphism class hash
e87c4acc4d1ba74b891d7a85f325b503e3a881bd5c2a4e49d4518c35ef3f3260
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 166 (nullity 55) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 21:46:40
Display reorder
181,55,3,131,58,73,138,155,66,142,159,44,162,39,122,100,164,85,89,25,115,60,95,70,140,173,43,52,160,47,56,76,134,154,12,96,110,40,15,24,113,63,91,106,35,46,2,133,10,139,78,145,72,149,168,59,169,48,80,137,158,141,75,54,65,151,127,88,124,156,13,38,165,31,28,104,99,94,32,109,105,23,21,18,86,83,62,120,34,42,14,116,29,101,90,61,118,111,161,19,170,9,77,71,171,128,132,50,143,147,152,129,135,167,53,57,172,8,4,74,67,125,30,102,92,11,41,33,107,97,87,64,36,197,196,180,187,186,208,205,192,193,190,191,182,183,204,207,188,189,176,177,209,206,195,194,200,201,202,203,178,185,199,179,184,198,214,215,216,219,218,217,210,213,212,211,220,1,16,98,27,114,121,82,93,103,163,37,157,6,69,79,175,150,146,51,136,130,126,148,144,166,49,45,174,5,7,81,68,153,26,112,119,0,17,22,108,117,84,123,20 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#12c36c7b075c404ad1fd3f656ab357d26cf582121b46d12c1b704537376fe22b, M = {2} 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: 221.

last edited by qawbecrdtey at 2026-10-01 21:46:41 · history