Equation 677 Database

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Magma 960ed3b135bf…

magma 960ed3b135bf
Size
273
Isomorphism class hash
960ed3b135bfc32f9077cd6af9897549899db097f9f5b7e5cf82afc6f5b65371
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 10:47:33
Display reorder
63,64,65,62,60,61,69,70,71,68,66,67,254,83,56,86,228,81,54,84,229,82,55,85,230,79,59,89,231,80,57,87,232,78,58,88,233,74,51,92,234,72,52,90,235,73,53,91,236,77,50,95,237,75,48,93,238,76,49,94,239,266,260,259,265,46,199,223,168,47,200,224,169,45,198,222,170,42,202,226,171,43,203,227,172,44,201,225,173,37,197,221,174,38,195,219,175,36,196,220,176,40,193,217,177,41,194,218,178,39,192,216,179,258,264,263,257,204,186,142,13,205,187,143,14,206,188,141,12,207,189,138,16,208,190,139,17,209,191,140,15,210,184,133,19,211,185,134,20,212,183,132,18,213,180,136,22,214,181,137,23,215,182,135,21,261,271,272,262,1,164,126,243,0,162,127,244,2,163,128,245,3,167,129,242,4,165,130,240,5,166,131,241,6,159,124,247,7,160,125,248,8,161,123,249,9,158,120,250,10,156,121,246,11,157,122,251,267,270,269,268,155,102,117,24,153,103,118,25,154,104,119,26,151,105,116,27,152,106,114,28,150,107,115,29,146,100,108,30,144,101,109,31,145,99,110,32,149,96,111,33,147,97,112,34,148,98,113,35,256,255,253,252 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#954a2425e38b1f8d73f83d01c811c18c22a6cf13713c169e64792ee66a752510, M = {0, 5, 10, 16, 21, 26, 30, 35, 41, 46, 51, 56, 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 10:47:34 · history