Equation 677 Database

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Magma 805daba8400d…

magma 805daba8400d
Size
273
Isomorphism class hash
805daba8400da35f9a91631e2f05f2bcf7b23ad25163b31d92de337d082a5780
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 22:53:30
Display reorder
52,53,51,48,49,50,58,59,57,54,55,56,254,44,22,5,228,42,23,3,229,43,21,4,230,47,18,0,231,45,19,2,232,46,20,1,233,39,13,11,234,40,14,9,235,41,12,10,236,38,16,7,237,36,17,8,238,37,15,6,239,266,260,259,265,35,199,223,168,33,200,224,169,34,198,222,170,31,202,226,171,32,203,227,172,30,201,225,173,26,197,221,174,24,195,219,175,25,196,220,176,29,193,217,177,27,194,218,178,28,192,216,179,258,264,263,257,186,106,142,204,187,107,143,205,188,105,141,206,189,102,138,207,190,103,139,208,191,104,140,209,184,97,133,210,185,98,134,211,183,96,132,212,180,100,136,213,181,101,137,214,182,99,135,215,261,271,272,262,91,164,126,243,92,162,127,244,90,163,128,245,94,167,129,242,95,165,130,240,93,166,131,241,89,159,124,247,87,160,125,248,88,161,123,249,85,158,120,250,86,156,121,246,84,157,122,251,267,270,269,268,155,60,117,83,153,61,118,81,154,62,119,82,151,63,116,79,152,64,114,80,150,65,115,78,146,66,108,74,144,67,109,72,145,68,110,73,149,69,111,77,147,70,112,75,148,71,113,76,256,255,253,252 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#b82bea23d952545bcb5d6b6a0cc235694bb3bc5cc3b3a153b6c38e307d02b955, M = {0, 5, 10, 16, 21, 26, 30, 35, 40, 46, 51, 56, 60} 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 22:53:31 · history