Equation 677 Database

← all  ·  ← by size  ·  ← size 273

Magma 8193ae664b3c…

magma 8193ae664b3c
Size
273
Isomorphism class hash
8193ae664b3c298fd0822009fa13fe56f01ac20967803ee3abcd39d30f72ed66
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 12:01:09
Display reorder
21,22,23,20,18,19,12,13,14,15,16,17,272,200,215,190,198,213,191,199,214,189,203,211,186,201,212,187,202,210,188,195,206,181,196,204,182,197,205,180,209,194,184,207,192,185,208,193,183,224,222,223,227,225,226,219,220,217,218,216,221,271,256,257,270,143,101,121,141,99,122,142,100,120,139,97,124,140,98,125,138,96,123,134,107,127,132,105,128,133,106,126,103,137,130,104,135,131,102,136,129,116,114,115,119,117,118,111,112,109,110,108,113,258,268,269,259,61,82,48,62,83,49,60,81,50,64,78,51,65,79,52,63,80,53,67,73,54,68,74,55,66,72,56,76,70,57,77,71,58,75,69,59,91,92,90,94,95,93,89,87,84,85,86,88,261,265,264,260,3,232,154,4,233,155,5,231,153,2,228,150,1,229,151,0,230,152,9,238,145,10,239,146,11,237,144,234,8,148,235,6,149,236,7,147,245,240,243,250,246,248,247,249,242,244,241,251,267,262,263,266,163,26,172,164,24,173,162,25,171,166,29,168,167,27,169,165,28,170,161,32,178,159,30,179,160,31,177,35,157,174,33,158,175,34,156,176,41,39,40,37,38,36,47,45,42,43,44,46,255,254,252,253 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#adb39c7b26968070fd85ec3ca227f43c35cfd242a3390aaf8597bfe24e1ed89b, M = {0, 5, 9, 12, 16, 20, 26, 30, 34, 38, 42, 46, 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 12:01:11 · history