Equation 677 Database

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Magma 74a029c8a6ff…

magma 74a029c8a6ff
Size
273
Isomorphism class hash
74a029c8a6ff813de4d26a954a2b69442945b0b7313bd549c13cda1d8b5a0417
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
2026-10-06 14:14:11
Display reorder
90,91,92,93,94,95,88,89,87,84,85,86,254,97,110,228,2,1,98,108,229,96,0,109,230,100,5,113,231,101,3,111,232,99,4,112,233,103,8,116,234,6,104,114,235,7,102,115,236,106,11,119,237,107,9,117,238,105,10,118,239,266,260,259,265,53,199,149,223,224,51,200,147,52,222,198,148,49,226,202,145,50,227,203,146,48,225,201,144,59,221,197,155,219,57,195,153,220,58,196,154,55,217,193,151,56,218,194,152,54,216,192,150,258,264,263,257,24,159,61,204,205,25,160,62,26,206,161,60,27,207,158,64,28,208,156,65,29,209,157,63,30,210,165,67,211,31,166,68,212,32,167,66,33,213,164,70,34,214,162,71,35,215,163,69,261,271,272,262,181,134,243,12,13,182,132,244,180,14,133,245,184,15,137,242,185,16,135,240,183,17,136,241,187,18,140,247,19,188,138,248,20,186,139,249,190,21,143,250,191,22,141,246,189,23,142,251,267,270,269,268,174,74,38,128,126,175,72,36,176,127,73,37,177,131,77,41,178,129,75,39,179,130,76,40,172,123,80,44,124,173,78,42,125,171,79,43,168,122,83,47,169,120,81,45,170,121,82,46,256,252,253,255 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#69e303b0df9a949f679bcb1932ca3e0d44707fb71c41006ed01ea0a3f8179ab7, M = {0, 5, 12, 15, 20, 25, 33, 38, 40, 48, 53, 58, 61} 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 2026-10-06 14:14:13 · history