Equation 677 Database

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Magma 5b1b2e0638b3…

magma 5b1b2e0638b3
Size
287
Isomorphism class hash
5b1b2e0638b349251cf7ee87f2dbff19e640819bb5624d17ca0cfa5b4bbde2bd
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 286) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 08:20:52
Display reorder
280,281,282,283,284,285,286,14,13,15,12,8,9,10,11,50,53,54,55,52,48,49,51,93,90,94,95,92,88,89,91,130,133,134,135,132,128,129,131,172,173,171,174,175,169,170,168,214,213,211,215,212,208,209,210,278,252,271,265,272,273,274,242,18,17,19,16,21,22,23,20,63,57,58,59,56,61,62,60,97,103,98,99,96,101,102,100,143,137,138,139,136,141,142,140,177,178,183,179,176,181,182,180,218,217,220,219,216,221,222,223,276,240,255,267,256,253,266,254,25,31,24,30,28,26,29,27,69,71,65,64,70,68,66,67,111,109,105,104,110,108,106,107,149,151,145,144,150,148,146,147,191,189,190,185,184,186,187,188,225,231,227,224,230,228,226,229,277,258,243,269,259,260,268,257,6,5,7,4,1,0,2,3,42,45,46,47,44,41,40,43,85,82,86,87,84,81,80,83,122,125,126,127,124,121,120,123,164,165,163,166,167,161,162,160,206,205,203,207,204,200,201,202,275,250,245,246,251,241,244,249,32,35,33,34,38,39,36,37,76,75,72,73,74,78,79,77,115,116,112,113,114,118,119,117,156,152,153,154,155,158,159,157,195,192,196,193,194,198,199,197,232,235,236,233,234,237,238,239,279,264,261,262,247,248,263,270 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 287 = 7 + 5*56, 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#e83035650a112a4626b8c7ce1675cd9b58ab3b164a3e70252b4d03aa47124247, M = {56, 57, 58, 59, 60, 61, 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, 56): MacNeish's product over GF(8) x GF(7); GF(8) = F_2[x]/(x^3 + 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: 1.

last edited by qawbecrdtey at 2026-10-07 08:20:53 · history