Equation 677 Database

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Magma 42d3910b3147…

magma 42d3910b3147
Size
293
Isomorphism class hash
42d3910b31473bd07eaf35f48e3d6033660baae7c5ab6c109925ecd4fcab0bc2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 292) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-09 12:31:31
Display reorder
22,31,29,30,27,28,21,25,23,24,26,20,292,242,243,239,240,241,245,244,247,246,248,249,250,251,238,153,150,151,152,149,148,147,141,142,140,144,145,143,146,59,58,83,61,60,82,81,80,79,77,78,75,76,74,69,70,71,72,73,68,264,263,265,266,259,260,261,262,109,110,105,103,104,108,111,107,106,88,89,87,84,85,86,93,94,92,90,91,101,98,99,100,97,95,96,102,185,186,182,184,183,187,189,188,178,176,177,181,179,180,19,17,14,15,16,18,287,286,288,289,290,283,284,285,211,209,217,215,216,214,210,213,212,204,205,203,207,208,206,201,202,200,198,199,230,229,227,228,225,226,224,231,56,57,44,55,54,51,53,52,42,43,41,38,39,40,32,33,37,35,36,34,282,281,275,276,277,278,279,280,8,9,11,12,13,7,10,6,5,2,0,1,4,3,160,159,157,158,154,156,175,165,166,164,168,169,167,171,172,170,155,174,173,161,163,162,232,233,234,235,236,237,65,66,63,64,62,67,291,258,252,253,254,255,256,257,131,132,137,138,139,130,133,129,128,123,124,125,126,127,223,220,221,222,219,218,197,191,192,190,194,195,193,196,113,112,122,115,114,134,136,135,121,119,120,117,118,116,46,47,48,49,50,45,274,273,267,268,269,270,271,272 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 293 = 13 + 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#ae850597310ca1e4e432d9166a7108f5487ce49948bce500209d7acd9fde2b9f, M = {7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 40, 41, 68} 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 2026-10-09 12:31:32 · history