Equation 677 Database

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Magma b0bb539ac1c2…

magma b0bb539ac1c2
Size
273
Isomorphism class hash
b0bb539ac1c21397e5cd3253d9050e566226e330d90f922b5bfd7aab4190a45a
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 12:47:33
Display reorder
2,1,0,5,3,4,8,6,7,11,9,10,254,36,14,228,25,26,37,12,229,38,24,13,230,39,28,17,231,40,29,15,232,41,27,16,233,42,31,20,234,43,32,18,235,19,44,30,236,45,34,23,237,46,35,21,238,47,33,22,239,266,260,259,265,101,199,149,223,224,99,200,147,100,222,198,148,97,226,202,145,98,227,203,146,96,225,201,144,107,221,197,155,105,219,195,153,196,106,220,154,103,217,193,151,104,218,194,152,102,216,192,150,258,264,263,257,112,68,204,159,160,113,66,205,111,161,67,206,108,158,71,207,109,156,69,208,110,157,70,209,118,165,63,210,119,166,64,211,65,117,167,212,114,164,62,213,115,162,60,214,116,163,61,215,261,271,272,262,181,134,243,59,57,182,132,244,180,58,133,245,184,55,137,242,185,56,135,240,183,54,136,241,187,50,140,247,188,48,138,248,139,186,49,249,190,53,143,250,191,51,141,246,189,52,142,251,267,270,269,268,174,75,86,128,126,175,76,84,176,127,77,85,177,131,74,89,178,129,72,87,179,130,73,88,172,123,81,92,173,124,82,90,83,171,125,91,168,122,80,95,169,120,78,93,170,121,79,94,256,252,253,255 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#58666f8071d01f531e6f0c3147dedbb33da52b01b6615c3c73eb980e964d7179, M = {0, 5, 12, 15, 20, 25, 31, 36, 42, 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 12:47:35 · history