Equation 677 Database

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Magma 7005ab4c915b…

magma 7005ab4c915b
Size
273
Isomorphism class hash
7005ab4c915b28fa4da374b3f320a102cae56e620a6e005d03673cd18189b6bf
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 04:10:01
Display reorder
38,36,37,41,39,40,44,42,43,47,45,46,254,51,109,104,228,52,110,102,229,108,103,230,53,112,50,107,231,113,48,105,232,111,49,106,233,57,115,99,234,58,116,100,235,59,114,101,236,118,56,98,237,119,54,96,238,117,55,97,239,266,260,259,265,199,95,223,168,200,93,224,169,94,222,170,198,91,202,226,171,92,203,227,172,90,201,225,173,197,86,221,174,195,84,219,175,196,85,220,176,89,193,217,177,87,194,218,178,88,192,216,179,258,264,263,257,143,186,72,204,141,187,73,205,188,74,206,142,189,139,75,207,190,140,76,208,191,138,77,209,134,184,78,210,132,185,79,211,133,183,80,212,180,137,81,213,181,135,82,214,182,136,83,215,261,271,272,262,164,125,61,243,162,123,62,244,124,60,245,163,121,167,64,242,122,165,65,240,120,166,63,241,159,131,67,247,160,129,68,248,161,130,66,249,127,158,70,250,128,156,71,246,126,157,69,251,267,270,269,268,155,18,4,29,153,19,5,27,20,3,28,154,21,151,1,25,22,152,0,26,23,150,2,24,146,16,10,35,144,17,11,33,145,15,9,34,12,149,6,31,13,147,7,32,14,148,8,30,256,255,253,252 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#59c0dab3d55e83047c113809dcb6925b23956e0c747f2365bb6fbba97ebd5493, M = {0, 5, 11, 15, 20, 25, 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 2026-10-08 04:10:02 · history