Equation 677 Database

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Magma be6b4f043a61…

magma be6b4f043a61
Size
273
Isomorphism class hash
be6b4f043a61c5c0a060ea1b8c544db3758025700be07faceb8374826b9f314c
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
2026-10-07 14:32:13
Display reorder
80,78,79,83,81,82,75,76,77,74,72,73,272,181,201,135,182,202,136,180,137,203,184,200,134,185,198,132,183,199,133,187,192,141,188,193,142,186,194,143,190,195,140,191,196,138,189,197,139,212,210,211,215,213,214,207,208,205,206,204,209,271,256,257,270,104,116,92,102,114,90,103,91,115,107,119,95,105,117,93,106,118,94,99,111,87,100,112,88,101,113,89,98,110,86,96,108,84,97,109,85,127,128,126,130,131,129,125,123,120,121,122,124,258,269,268,259,149,163,7,147,164,8,148,6,162,145,166,10,146,167,11,144,165,9,155,161,5,153,159,3,154,160,4,151,157,0,152,158,2,150,156,1,170,168,169,173,171,172,176,174,178,179,177,175,261,265,264,260,219,228,20,220,229,18,221,19,230,218,231,23,216,232,21,217,233,22,225,234,15,226,235,16,227,236,17,224,237,14,222,238,12,223,239,13,245,240,243,250,246,248,247,249,242,244,241,251,267,262,263,266,32,44,68,30,42,66,31,67,43,35,47,71,33,45,69,34,46,70,27,39,63,28,40,64,29,41,65,26,38,62,24,36,60,25,37,61,54,55,56,57,58,59,52,53,50,48,49,51,254,252,253,255 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#38a4e23a99caaa7b44b0fde217361d7389ff59fad772c7ae239f5a60818fe03a, M = {0, 4, 10, 13, 16, 20, 24, 28, 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 2026-10-07 14:32:15 · history