Equation 677 Database

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Magma 0a2a5c9617a5…

magma 0a2a5c9617a5
Size
273
Isomorphism class hash
0a2a5c9617a5e051df3d4b8295b52609a39baf80978a3bdeb417dbe0a94956f1
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 15:46:42
Display reorder
75,76,77,74,72,73,81,82,83,80,78,79,254,66,1,228,85,86,67,0,229,68,84,2,230,88,69,3,231,89,70,4,232,87,71,5,233,64,91,6,234,65,92,7,235,63,90,8,236,60,94,9,237,61,95,10,238,62,93,11,239,266,260,259,265,223,199,148,59,57,224,200,149,222,58,198,147,55,226,202,144,56,227,203,145,54,225,201,146,221,50,197,154,219,48,195,155,220,49,196,153,217,53,193,150,218,51,194,151,216,52,192,152,258,264,263,257,160,111,25,204,205,161,112,26,159,206,113,24,207,156,110,28,208,157,108,29,209,158,109,27,166,210,117,31,167,211,118,32,165,212,119,30,162,213,116,34,163,214,114,35,164,215,115,33,261,271,272,262,181,134,243,99,100,182,132,244,180,101,133,245,98,184,137,242,96,185,135,240,97,183,136,241,187,105,140,247,188,106,138,248,186,107,139,249,190,104,143,250,191,102,141,246,189,103,142,251,267,270,269,268,128,37,14,174,175,126,38,12,127,176,36,13,177,131,40,17,178,129,41,15,179,130,39,16,123,172,43,20,124,173,44,18,125,171,42,19,122,168,46,23,120,169,47,21,121,170,45,22,256,252,253,255 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#0f0ec421cc32f9c063215c008f5f1d2db6033828d1c93d9b7da541d2d3cf51f3, M = {0, 5, 12, 16, 21, 26, 31, 36, 41, 45, 50, 55, 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 2026-10-08 15:46:43 · history