Equation 677 Database

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Magma 9359a1a05cca…

magma 9359a1a05cca
Size
273
Isomorphism class hash
9359a1a05cca58e123f3bcb2b178988b0711145380d77d5aacc0c90195ad9b0d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 272) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 20:11:47
Display reorder
96,97,98,99,100,101,102,103,104,105,106,107,254,94,27,76,228,95,77,28,229,93,75,29,230,90,72,26,231,91,73,24,232,92,74,25,233,33,85,82,234,34,86,83,235,35,84,81,236,32,88,78,237,30,89,79,238,31,87,80,239,266,260,259,265,64,223,199,149,65,200,224,147,63,198,222,148,60,202,226,145,61,203,227,146,62,201,225,144,221,70,197,155,219,71,195,153,220,69,196,154,217,66,193,151,218,67,194,152,216,68,192,150,258,264,263,257,48,112,159,204,49,160,113,205,50,161,111,206,51,158,108,207,52,156,109,208,53,157,110,209,118,54,165,210,119,55,166,211,117,56,167,212,114,57,164,213,115,58,162,214,116,59,163,215,261,271,272,262,36,181,134,243,37,132,182,244,38,133,180,245,39,137,184,242,40,135,185,240,41,136,183,241,187,42,140,247,188,43,138,248,186,44,139,249,190,45,143,250,191,46,141,246,189,47,142,251,267,270,269,268,127,176,15,8,128,16,174,6,126,17,175,7,130,14,179,11,131,12,177,9,129,13,178,10,171,125,21,3,172,123,22,4,173,124,23,5,170,121,20,2,168,122,18,1,169,120,19,0,256,255,253,252 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 273 = 13 + 5*52, 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#33430dadf8546adceaddacfc75eeb6c00258f5413ce1926e16e948db7c79b4f3, M = {0, 5, 10, 16, 21, 26, 30, 35, 40, 46, 51, 56, 63} 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, 52): MacNeish's product over GF(4) x GF(13); 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 2026-10-07 20:11:48 · history