Equation 677 Database

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Magma 6ebd25188cbe…

magma 6ebd25188cbe
Size
273
Isomorphism class hash
6ebd25188cbed3b4ea80135034d80fe90b16a609bd6a11cf35d1e52931d99369
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
2026-10-09 01:23:22
Display reorder
36,37,38,39,40,41,42,43,44,45,46,47,254,30,10,50,228,31,11,48,229,32,9,49,230,33,6,53,231,34,7,51,232,35,8,52,233,28,0,56,234,29,2,54,235,27,1,55,236,24,4,59,237,25,5,57,238,26,3,58,239,266,260,259,265,23,199,223,168,21,200,224,169,22,198,222,170,19,202,226,171,20,203,227,172,18,201,225,173,14,197,221,174,12,195,219,175,13,196,220,176,17,193,217,177,15,194,218,178,16,192,216,179,258,264,263,257,186,106,142,204,187,107,143,205,188,105,141,206,189,102,138,207,190,103,139,208,191,104,140,209,184,97,133,210,185,98,134,211,183,96,132,212,180,100,136,213,181,101,137,214,182,99,135,215,261,271,272,262,91,164,126,243,92,162,127,244,90,163,128,245,94,167,129,242,95,165,130,240,93,166,131,241,89,159,124,247,87,160,125,248,88,161,123,249,85,158,120,250,86,156,121,246,84,157,122,251,267,270,269,268,155,68,117,83,153,66,118,81,154,67,119,82,151,71,116,79,152,69,114,80,150,70,115,78,146,63,108,74,144,64,109,72,145,65,110,73,149,62,111,77,147,60,112,75,148,61,113,76,256,255,253,252 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#c2d2ffbf4b11c3cb3cbc2e9e264bf213176e8d1ad1040891146c21601605ebcd, M = {0, 5, 10, 15, 20, 25, 30, 35, 40, 46, 51, 56, 60} 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 2026-10-09 01:23:23 · history