Equation 677 Database

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Magma 330db42a574c…

magma 330db42a574c
Size
273
Isomorphism class hash
330db42a574c1c35ff084de9e1a881a07a0f6c29c121f48f564743d4ba795510
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 08:35:08
Display reorder
59,57,58,55,56,54,50,48,49,53,51,52,254,1,42,62,228,60,0,43,229,2,61,44,230,65,3,45,231,63,4,46,232,64,5,47,233,6,40,68,234,11,41,66,235,10,39,67,236,7,36,71,237,8,37,69,238,9,38,70,239,266,260,259,265,199,223,146,99,144,200,224,100,198,145,222,101,149,202,226,98,147,203,227,96,148,201,225,97,197,221,152,105,195,219,150,106,196,220,151,107,193,217,155,104,194,218,153,102,192,216,154,103,258,264,263,257,113,160,204,84,205,111,161,85,112,206,159,86,207,109,156,87,208,110,157,88,209,108,158,89,119,166,210,90,117,167,211,91,118,165,212,92,115,162,213,93,116,163,214,94,114,164,215,95,261,271,272,262,72,180,139,243,140,73,181,244,74,138,182,245,142,75,183,242,143,76,184,240,141,77,185,241,78,186,137,247,79,187,135,248,80,188,136,249,81,189,133,250,82,190,134,246,83,191,132,251,267,270,269,268,32,129,33,176,35,34,130,174,31,30,131,175,24,25,128,179,27,26,126,177,29,28,127,178,14,120,15,171,16,121,17,172,12,122,13,173,21,123,20,170,22,124,23,168,19,125,18,169,256,255,253,252 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#9c565a9fd79b154e390f38dd387d90fedf9817e0675733b83815c4693870456f, M = {0, 6, 12, 16, 21, 26, 30, 35, 40, 45, 50, 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 2026-10-06 08:35:16 · history