Equation 677 Database

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Magma d89486c35034…

magma d89486c35034
Size
273
Isomorphism class hash
d89486c35034ba69e4a1b9afb59a9011f00489e88cbf44a2cf1eca90ee74b8fe
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
2026-10-06 15:02:23
Display reorder
27,28,29,26,24,25,33,34,35,32,30,31,272,60,72,39,40,61,73,41,62,74,63,38,75,64,36,76,65,37,77,66,78,45,67,79,46,68,80,47,81,69,44,70,82,42,71,83,43,56,54,55,59,57,58,51,52,49,50,48,53,263,259,257,271,144,157,172,173,145,158,171,146,156,147,168,160,148,169,161,149,170,159,150,163,178,151,164,179,152,162,177,166,153,174,154,167,175,155,165,176,140,138,139,143,141,142,135,136,133,134,132,137,258,269,270,256,111,123,89,87,112,124,88,113,125,110,85,122,108,86,120,109,84,121,117,129,95,118,130,93,119,131,94,128,116,91,114,126,92,115,127,90,107,105,106,103,104,102,98,96,100,101,99,97,262,260,264,261,1,13,185,183,0,14,184,2,12,3,181,16,4,182,17,5,180,15,6,19,191,7,20,189,8,18,190,22,9,187,10,23,188,11,21,186,201,202,203,200,198,199,192,193,197,195,196,194,266,267,265,268,216,230,248,246,217,228,247,218,229,219,251,233,220,249,231,221,250,232,222,236,243,223,234,244,224,235,245,239,225,242,226,237,240,227,238,241,212,210,211,215,213,214,207,208,205,206,204,209,255,252,253,254 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#a08efb2611f2171bf6f734a20baed2f33f3141d650739b05e30e32bcbe11c9bc, M = {0, 4, 8, 12, 16, 20, 26, 30, 34, 38, 42, 46, 61} 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 2026-10-06 15:02:24 · history