Equation 677 Database

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Magma 10447df72cf9…

magma 10447df72cf9
Size
221
Isomorphism class hash
10447df72cf9c2774f0701bb3a5eb3d3b397129f7da08756e276420314dc0718
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 21:46:08
Display reorder
220,19,158,39,59,79,94,119,139,74,99,114,134,154,14,34,54,161,160,162,163,164,165,166,167,89,109,129,149,9,29,49,69,124,144,4,24,44,64,84,104,219,209,214,204,18,157,38,58,78,93,118,138,73,98,113,133,153,13,33,53,193,195,196,198,184,187,189,191,88,108,128,148,8,28,48,68,123,143,3,23,43,63,83,103,217,208,213,203,17,159,37,57,75,92,117,137,72,97,112,132,152,12,32,52,176,177,178,179,180,181,182,183,87,107,127,147,7,27,47,67,122,142,2,22,42,62,82,102,218,207,212,202,16,155,36,55,77,90,116,136,71,95,110,130,150,11,31,50,192,194,197,199,185,186,188,190,85,105,125,146,5,25,45,65,120,140,1,21,40,60,80,100,216,206,211,201,15,156,35,56,76,91,115,135,70,96,111,131,151,10,30,51,174,175,168,169,170,171,172,173,86,106,126,145,6,26,46,66,121,141,0,20,41,61,81,101,215,205,210,200 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#05aba89c8fda3d45fa6b247c3cfa1978c014a8edff02986eef8d4cfb39f715ed, M = {41} 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 21:46:09 · history