Equation 677 Database

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Magma 9656dcaf3612…

magma 9656dcaf3612
Size
273
Isomorphism class hash
9656dcaf3612a1dc82d0204fe138c0b32187a49ccce95cf5f024df5dca7b488b
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 20:29:16
Display reorder
66,67,68,69,70,71,64,65,63,60,61,62,254,52,83,228,87,53,88,81,229,51,89,82,230,48,86,79,231,49,84,80,232,50,85,78,233,93,58,74,234,94,59,72,235,95,57,73,236,54,92,77,237,55,90,75,238,56,91,76,239,266,260,259,265,12,199,149,223,13,224,200,147,14,222,198,148,15,226,202,145,16,227,203,146,17,225,201,144,221,18,197,155,219,19,195,153,220,20,196,154,21,217,193,151,22,218,194,152,23,216,192,150,258,264,263,257,4,159,204,112,5,113,160,205,3,111,161,206,1,108,158,207,0,109,156,208,2,110,157,209,118,10,165,210,119,11,166,211,117,9,167,212,6,114,164,213,7,115,162,214,8,116,163,215,261,271,272,262,181,134,243,98,182,96,132,244,180,97,133,245,184,101,137,242,185,99,135,240,183,100,136,241,104,187,140,247,102,188,138,248,103,186,139,249,190,107,143,250,191,105,141,246,189,106,142,251,267,270,269,268,174,25,38,128,175,126,26,36,176,127,24,37,177,131,28,41,178,129,29,39,179,130,27,40,123,172,31,44,124,173,32,42,125,171,30,43,168,122,34,47,169,120,35,45,170,121,33,46,256,252,253,255 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#b24873ef385d9876d07add1b0ccd1e5b9965acff1b69e8225210d446f480d74b, M = {0, 5, 10, 16, 21, 26, 33, 38, 43, 48, 53, 58, 62} 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 20:29:17 · history