Equation 677 Database

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Magma 241590ae1c06…

magma 241590ae1c06
Size
273
Isomorphism class hash
241590ae1c06efe280946b9c45bb59f62651874c5a35239a9d8b84020e166427
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
2026-10-08 18:28:13
Display reorder
120,121,122,123,124,125,126,127,128,129,130,131,253,135,109,5,228,110,3,229,136,137,108,4,230,134,112,0,231,132,113,2,232,133,111,1,233,115,141,11,234,142,116,9,235,143,114,10,236,140,118,7,237,138,119,8,238,139,117,6,239,266,260,259,265,49,221,211,161,219,212,159,50,48,220,210,160,52,217,214,157,53,218,215,158,51,216,213,156,227,55,209,167,56,225,207,165,54,226,208,166,58,223,205,163,59,224,206,164,57,222,204,162,258,264,263,257,66,77,171,39,75,172,40,67,68,76,173,41,69,73,170,38,70,74,168,36,71,72,169,37,83,64,177,45,65,81,178,46,63,82,179,47,60,79,176,44,61,80,174,42,62,78,175,43,261,271,272,262,193,104,146,243,102,144,244,194,192,103,145,245,196,107,149,242,197,105,147,240,195,106,148,241,99,199,152,247,200,100,150,248,198,101,151,249,202,98,155,250,203,96,153,246,201,97,154,251,267,270,269,268,186,93,18,29,94,19,27,187,188,95,20,28,189,92,21,25,190,90,22,26,191,91,23,24,84,184,16,35,185,85,17,33,183,86,15,34,180,87,12,31,181,88,13,32,182,89,14,30,256,254,255,252 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#47b26c2e0558f6c4fdff38c956d09d23d3aef780160b6fe0856dd3e8f07caf34, M = {0, 5, 10, 16, 21, 26, 33, 38, 43, 48, 53, 55, 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 2026-10-08 18:28:14 · history