Equation 677 Database

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Magma e8c40c592f5b…

magma e8c40c592f5b
Size
273
Isomorphism class hash
e8c40c592f5b2ecaae7e5b936799e112e768caeed3d76bb93ba20423cd3a033a
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 07:30:42
Display reorder
65,63,64,61,62,60,71,69,70,67,68,66,254,43,51,2,228,44,52,1,229,42,53,0,230,46,50,5,231,47,48,3,232,45,49,4,233,57,41,8,234,58,39,6,235,59,40,7,236,37,56,11,237,38,54,9,238,36,55,10,239,266,260,259,265,35,199,223,168,33,200,224,169,34,198,222,170,31,202,226,171,32,203,227,172,30,201,225,173,197,26,221,174,195,24,219,175,196,25,220,176,29,193,217,177,27,194,218,178,28,192,216,179,258,264,263,257,204,186,85,142,205,187,86,143,206,188,84,141,207,189,88,138,208,190,89,139,209,191,87,140,184,210,91,133,185,211,92,134,183,212,90,132,213,180,94,136,214,181,95,137,215,182,93,135,261,271,272,262,16,164,126,243,17,162,127,244,15,163,128,245,12,167,129,242,13,165,130,240,14,166,131,241,159,22,124,247,160,23,125,248,161,21,123,249,18,158,120,250,19,156,121,246,20,157,122,251,267,270,269,268,155,98,117,72,153,96,118,73,154,97,119,74,151,101,116,75,152,99,114,76,150,100,115,77,104,146,108,78,102,144,109,79,103,145,110,80,149,107,111,81,147,105,112,82,148,106,113,83,256,255,253,252 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#a687d51fdba056b88b615f4c33c4bd51079879725771af3a621b4a64ac93acf2, M = {0, 5, 10, 16, 21, 25, 32, 37, 42, 47, 52, 57, 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 2026-10-08 07:30:43 · history