Equation 677 Database

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Magma de4494d3dcc2…

magma de4494d3dcc2
Size
221
Isomorphism class hash
de4494d3dcc2305a22424728c95eea2757e6e954c15f83854e00532335ab8009
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 21:46:47
Display reorder
179,199,197,181,191,192,186,207,184,193,178,183,190,185,208,189,182,180,195,196,176,209,198,194,200,188,177,187,201,203,202,205,204,206,218,210,213,220,217,219,216,212,215,211,214,142,40,92,74,138,103,163,151,96,110,169,35,155,4,128,122,68,130,108,117,7,83,100,82,1,32,172,57,157,50,162,17,15,86,133,42,29,24,89,150,9,137,114,11,109,3,116,127,65,121,158,67,113,132,170,49,63,43,105,78,141,75,144,99,0,81,154,91,25,14,159,55,173,31,166,47,39,70,124,53,28,37,95,72,21,85,149,48,61,18,76,106,136,101,168,125,79,145,156,22,129,59,73,152,143,139,97,120,30,111,64,131,19,45,171,33,160,38,174,8,5,123,147,12,27,10,87,93,51,134,90,36,88,52,84,102,148,115,165,94,69,71,161,58,126,26,107,60,77,80,140,135,16,62,66,118,34,44,164,6,175,41,167,20,2,104,98,56,13,46,112,119,54,153,146,23 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 = {3} 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 21:46:48 · history