Equation 677 Database

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Magma a99af504b508…

magma a99af504b508
Size
273
Isomorphism class hash
a99af504b508dca950a217bb5c25932240f499d183e92cc2b9dd43a57236643e
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 18:23:03
Display reorder
214,213,215,212,210,211,204,205,206,207,208,209,263,45,46,47,44,42,43,36,37,38,39,40,41,161,159,160,157,158,156,167,165,166,163,164,162,53,51,52,49,50,48,59,57,58,55,56,54,112,113,111,108,109,110,118,119,117,114,115,116,262,259,257,267,22,23,21,18,19,20,13,14,12,16,17,15,107,105,106,103,104,102,98,96,97,101,99,100,197,195,196,193,194,192,203,201,202,199,200,198,154,155,153,150,151,152,145,146,144,148,149,147,256,270,271,258,183,184,185,182,180,181,189,190,191,188,186,187,140,138,139,143,141,142,135,136,137,134,132,133,33,34,35,32,30,31,24,25,26,27,28,29,85,86,84,88,89,87,91,92,90,94,95,93,260,272,265,266,66,67,68,69,70,71,64,65,63,60,61,62,79,80,78,82,83,81,77,75,76,73,74,72,120,121,122,123,124,125,126,127,128,129,130,131,176,174,175,179,177,178,171,172,173,170,168,169,261,268,264,269,219,220,221,218,216,217,225,226,227,224,222,223,232,233,231,228,229,230,238,239,237,234,235,236,244,245,243,240,241,242,250,251,249,246,247,248,10,11,9,6,7,8,0,2,1,4,5,3,252,253,255,254 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 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 2026-10-08 18:23:05 · history