Equation 677 Database

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Magma 5e7d2c0dd110…

magma 5e7d2c0dd110
Size
221
Isomorphism class hash
5e7d2c0dd110d9593a3a6f5c7b44c4a12baa359944bbf2089c7ec03e363971dd
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 21:51:57
Display reorder
211,20,3,72,94,98,11,79,39,110,90,17,18,15,5,25,70,63,8,37,76,108,22,136,121,103,145,134,116,154,142,128,28,57,33,168,171,118,175,167,130,170,151,138,125,30,42,120,127,133,50,141,54,148,153,32,24,10,2,34,101,87,41,27,83,78,13,107,62,81,75,69,85,112,93,88,7,4,51,172,173,150,174,161,61,162,124,129,135,26,0,109,80,68,38,89,6,64,73,19,53,59,29,44,131,139,56,31,114,126,48,95,77,91,65,99,113,82,71,67,35,21,43,163,164,146,169,165,122,166,143,149,104,196,202,186,179,193,178,192,187,184,189,182,203,201,191,188,180,181,185,199,194,195,177,198,176,200,204,206,205,208,207,209,183,190,197,219,217,212,220,218,216,214,210,215,213,52,47,123,60,155,55,137,46,117,105,58,9,12,16,40,100,66,23,14,96,86,36,115,102,147,140,132,119,97,152,144,49,45,1,156,160,111,158,159,106,157,92,84,74 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 = {34} 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 21:51:57 · history