Equation 677 Database

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Magma fc823ad33dca…

magma fc823ad33dca
Size
273
Isomorphism class hash
fc823ad33dcae73c79a7d24371310cb803299b49c3cb97188546bd9bb4c859cd
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 04:46:48
Display reorder
35,33,34,31,32,30,26,24,25,29,27,28,254,69,37,74,228,70,38,72,229,71,36,73,230,68,40,77,231,66,41,75,232,67,39,76,233,60,80,43,234,61,78,44,235,62,79,42,236,63,83,46,237,64,81,47,238,65,82,45,239,266,260,259,265,97,199,223,149,98,200,224,147,96,198,222,148,100,202,226,145,101,203,227,146,99,201,225,144,103,221,197,155,104,219,195,153,102,220,196,154,106,217,193,151,107,218,194,152,105,216,192,150,258,264,263,257,115,159,0,204,116,160,2,205,114,161,1,206,118,158,4,207,119,156,5,208,117,157,3,209,113,7,165,210,111,8,166,211,112,6,167,212,109,10,164,213,110,11,162,214,108,9,163,215,261,271,272,262,181,134,52,243,182,132,53,244,180,133,51,245,184,137,48,242,185,135,49,240,183,136,50,241,187,58,140,247,188,59,138,248,186,57,139,249,190,54,143,250,191,55,141,246,189,56,142,251,267,270,269,268,174,91,125,12,175,92,123,13,176,90,124,14,177,94,121,15,178,95,122,16,179,93,120,17,172,131,89,18,173,129,87,19,171,130,88,20,168,127,85,21,169,128,86,22,170,126,84,23,256,255,253,252 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#d33e4a3e2f8aecd7db8c3ccbf48af948a122b54aec333d772566c797fe9ef74b, M = {0, 5, 10, 15, 20, 25, 30, 35, 40, 46, 51, 56, 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 04:46:50 · history