Equation 677 Database

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Magma 8021d9682f78…

magma 8021d9682f78
Size
273
Isomorphism class hash
8021d9682f78f0a1306bfc4773b453261188ac30514b511e3f0b26b9b386514c
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 14:27:05
Display reorder
44,42,43,47,45,46,39,40,41,38,36,37,254,9,33,18,228,10,19,34,229,11,20,35,230,21,8,32,231,22,6,30,232,23,7,31,233,1,24,16,234,0,25,17,235,2,26,15,236,3,27,12,237,4,28,13,238,5,29,14,239,266,260,259,265,199,223,146,67,200,144,224,68,198,145,222,66,149,202,226,70,147,203,227,71,148,201,225,69,197,221,152,65,195,219,150,63,196,220,151,64,193,217,155,61,194,218,153,62,192,216,154,60,258,264,263,257,72,160,204,111,73,205,161,112,74,206,159,113,207,75,156,110,208,76,157,108,209,77,158,109,78,166,210,117,79,167,211,118,80,165,212,119,81,162,213,116,82,163,214,114,83,164,215,115,261,271,272,262,138,180,99,243,139,100,181,244,140,101,182,245,98,141,183,242,96,142,184,240,97,143,185,241,136,186,105,247,137,187,106,248,135,188,107,249,132,189,104,250,133,190,102,246,134,191,103,251,267,270,269,268,84,59,128,176,85,126,57,174,86,127,58,175,131,87,55,179,129,88,56,177,130,89,54,178,90,50,123,171,91,48,124,172,92,49,125,173,93,53,122,170,94,51,120,168,95,52,121,169,256,255,253,252 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#fbd23cd98406f165f23d6b41307d902a92b7e2e110ccd89116da4983a4804a48, M = {0, 7, 12, 15, 20, 25, 31, 36, 41, 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 2026-10-08 14:27:06 · history