Equation 677 Database

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Magma ae7245be3ea7…

magma ae7245be3ea7
Size
273
Isomorphism class hash
ae7245be3ea78b73b9a408e2581e7ee258413fce5d529b3044d3ed9f295a3b8b
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 22:54:07
Display reorder
118,119,117,114,115,116,109,110,108,112,113,111,254,120,12,99,228,121,100,13,229,101,122,14,230,123,98,15,231,124,96,16,232,125,97,17,233,126,18,105,234,127,19,106,235,128,20,107,236,129,21,104,237,130,22,102,238,131,23,103,239,266,260,259,265,148,223,199,87,149,200,224,88,198,147,222,89,144,202,226,86,145,203,227,84,146,201,225,85,154,221,197,93,155,219,195,94,153,220,196,95,150,217,193,92,151,218,194,90,152,216,192,91,258,264,263,257,204,3,51,159,205,52,4,160,53,206,5,161,207,50,2,158,208,48,1,156,209,49,0,157,210,9,57,165,211,10,58,166,212,11,59,167,213,8,56,164,214,6,54,162,215,7,55,163,261,271,272,262,181,74,137,243,182,135,72,244,136,180,73,245,184,133,77,242,185,134,75,240,183,132,76,241,187,80,143,247,188,78,141,248,186,79,142,249,190,83,139,250,191,81,140,246,189,82,138,251,267,270,269,268,28,66,175,40,29,176,67,41,174,27,68,39,24,178,69,36,25,179,70,37,26,177,71,38,34,64,173,46,35,65,171,47,33,63,172,45,30,60,169,42,31,61,170,43,32,62,168,44,256,255,253,252 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#368900d303714df43b3718b8680935166fd1150994cfe143b7c0fba0a5b985be, M = {0, 5, 12, 16, 21, 26, 31, 36, 41, 46, 51, 56, 63} 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 22:54:12 · history