Equation 677 Database

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Magma 42f6a5b086be…

magma 42f6a5b086be
Size
273
Isomorphism class hash
42f6a5b086be9e1d970ca2fc7a23182d99cc23e07f4db0c0445caba9b494fdde
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 16:22:13
Display reorder
38,36,37,41,39,40,44,42,43,47,45,46,254,4,109,97,228,5,110,98,229,3,108,230,96,112,1,100,231,113,0,101,232,111,2,99,233,10,115,103,234,11,116,104,235,9,114,102,236,118,6,106,237,119,7,107,238,117,8,105,239,266,260,259,265,199,85,223,168,200,86,224,169,198,84,170,222,88,202,226,171,89,203,227,172,87,201,225,173,197,91,221,174,195,92,219,175,196,90,220,176,94,193,217,177,95,194,218,178,93,192,216,179,258,264,263,257,143,186,58,204,141,187,59,205,142,188,206,57,189,139,54,207,190,140,55,208,191,138,56,209,134,184,49,210,132,185,50,211,133,183,48,212,180,137,52,213,181,135,53,214,182,136,51,215,261,271,272,262,164,125,79,243,162,123,80,244,163,124,245,78,121,167,82,242,122,165,83,240,120,166,81,241,159,131,77,247,160,129,75,248,161,130,76,249,127,158,73,250,128,156,74,246,126,157,72,251,267,270,269,268,155,20,33,69,153,18,34,70,154,19,71,35,23,151,32,68,21,152,30,66,22,150,31,67,146,15,24,60,144,16,25,61,145,17,26,62,14,149,27,63,12,147,28,64,13,148,29,65,256,255,253,252 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#bc5f623c03e0cf031de7da5cba3786bb6161d1a009770b59759abcaaa846aef4, M = {0, 8, 12, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63} 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 16:22:14 · history