Equation 677 Database

← all  ·  ← by size  ·  ← size 293

Magma d6ec08eb56d4…

magma d6ec08eb56d4
Size
293
Isomorphism class hash
d6ec08eb56d4f484fd50df7eb651fc44647d2651e7a5e212e89180393cba02b0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 292) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 20:43:13
Display reorder
34,35,27,25,26,33,36,32,31,28,30,29,292,244,241,242,240,239,238,243,246,247,245,248,249,250,251,152,153,149,150,151,148,147,140,142,143,141,145,146,144,79,80,78,82,83,81,76,77,73,74,75,72,70,71,66,64,68,69,67,65,259,258,253,252,254,255,256,257,105,99,100,98,96,97,104,102,103,101,109,110,111,108,106,107,114,115,116,113,112,123,117,118,119,120,121,122,180,181,182,171,172,179,183,184,177,178,176,173,174,175,19,20,24,22,23,21,284,283,285,286,287,288,289,290,218,214,212,213,210,211,219,217,215,216,190,191,192,193,194,195,187,188,189,186,185,164,166,167,165,169,170,168,17,18,16,50,51,37,14,15,44,45,46,47,48,49,41,42,39,40,38,43,282,281,275,276,277,278,279,280,5,13,11,12,9,10,4,8,6,7,3,1,2,0,155,154,161,159,160,157,158,234,231,229,230,227,228,226,237,235,236,163,162,156,233,232,224,225,223,220,221,222,58,59,63,61,62,60,291,266,260,261,262,263,264,265,90,86,84,85,89,87,92,93,94,95,130,131,132,129,203,204,207,208,209,206,205,202,201,199,200,197,198,196,128,126,127,88,91,133,125,124,138,139,137,134,135,136,56,57,54,52,53,55,274,273,267,268,269,270,271,272 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 293 = 13 + 5*56, 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#ae850597310ca1e4e432d9166a7108f5487ce49948bce500209d7acd9fde2b9f, M = {0, 1, 2, 3, 4, 5, 6, 16, 17, 45, 46, 47, 68} 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, 56): MacNeish's product over GF(8) x GF(7); GF(8) = F_2[x]/(x^3 + 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: 1.

last edited by qawbecrdtey at 2026-10-07 20:43:14 · history