Equation 677 Database

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Magma 47a257cbacab…

magma 47a257cbacab
Size
273
Isomorphism class hash
47a257cbacab3b1b9a6eff1d75ae23aa97e5bffa092f0fc75a8e2750ff1b815b
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 17:15:27
Display reorder
48,49,50,51,52,53,54,55,56,57,58,59,272,92,78,103,90,79,104,91,80,102,81,95,106,93,107,82,83,94,105,101,87,76,99,88,77,100,89,75,97,86,72,98,84,73,96,85,74,62,60,61,65,63,64,68,66,70,71,69,67,271,257,259,263,38,27,15,36,28,16,37,29,17,26,41,14,39,12,24,25,40,13,21,44,33,22,42,34,23,43,35,20,47,32,18,45,30,19,46,31,5,3,4,0,2,1,11,9,6,7,8,10,256,270,269,258,140,126,151,138,127,152,139,128,150,129,143,154,141,155,130,131,142,153,149,135,124,147,136,125,148,137,123,145,134,120,146,132,121,144,133,122,110,108,109,113,111,112,116,114,118,119,117,115,261,264,260,262,199,188,162,200,186,163,198,187,164,191,202,165,203,166,189,190,201,167,160,197,183,161,195,184,159,196,185,156,193,182,157,194,180,158,192,181,175,176,174,178,179,177,173,171,168,169,170,172,268,265,267,266,234,217,248,235,218,246,236,216,247,220,237,251,238,249,221,219,239,250,243,232,223,244,233,224,245,231,222,242,228,226,240,229,227,241,230,225,205,206,204,208,209,207,211,212,213,214,215,210,254,253,252,255 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#d999f02d519da9e6482c93589338b3231f65cc1ce6e36c19968e5d782b765397, M = {0, 4, 8, 12, 16, 20, 25, 29, 32, 37, 41, 45, 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 17:15:28 · history