Equation 677 Database

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Magma 9b3cb05c8afe…

magma 9b3cb05c8afe
Size
273
Isomorphism class hash
9b3cb05c8afee9baac7ef69b79cfcc87d395054cee22665e99205d3aac4835bb
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 12:57:52
Display reorder
0,2,1,4,5,3,7,8,6,10,11,9,272,55,44,33,56,34,42,54,35,43,58,47,32,59,45,30,57,31,46,53,39,24,51,25,40,52,26,41,49,38,27,50,28,36,48,29,37,20,18,19,23,21,22,15,16,13,14,12,17,263,259,257,271,155,186,178,153,179,187,154,177,188,151,189,174,152,190,175,150,176,191,146,184,169,144,170,185,145,168,183,149,180,172,147,173,181,148,171,182,162,163,164,165,166,167,160,161,158,156,157,159,258,269,270,256,130,119,104,131,102,117,129,103,118,126,115,107,127,116,105,128,106,114,121,110,99,122,100,108,120,101,109,124,113,98,125,96,111,123,97,112,140,138,139,143,141,142,135,136,133,134,132,137,262,260,264,261,68,197,91,66,92,195,67,90,196,71,193,94,69,194,95,70,93,192,63,203,89,64,87,201,65,88,202,62,199,85,60,86,200,61,84,198,82,83,81,78,79,80,73,74,75,76,77,72,266,267,265,268,214,248,237,215,238,246,213,239,247,210,251,236,211,249,234,212,235,250,205,243,228,206,229,244,204,230,245,208,242,231,209,232,240,207,233,241,224,222,223,227,225,226,219,220,217,218,216,221,252,255,254,253 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#e9460cea3e471d03fe1a4dfa5e68e64aa509c8601c2a885c863435b22f6faffe, M = {0, 4, 8, 12, 16, 20, 24, 29, 33, 37, 41, 44, 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 12:57:53 · history