Equation 677 Database

← all  ·  ← by size  ·  ← size 273

Magma 45826b9fd983…

magma 45826b9fd983
Size
273
Isomorphism class hash
45826b9fd98374f62398d1f255eb293e994e8af34425ebed40c0de4ab9f7c152
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 08:10:35
Display reorder
71,69,70,67,68,66,62,60,61,65,63,64,254,55,45,8,228,56,46,6,229,47,7,230,54,44,58,11,231,42,59,9,232,43,57,10,233,36,53,3,234,4,37,51,235,38,52,5,236,39,49,2,237,40,50,1,238,41,48,0,239,266,260,259,265,199,111,223,168,200,112,224,169,113,222,170,198,110,202,226,171,108,203,227,172,109,201,225,173,117,197,221,174,219,118,195,175,119,196,220,176,116,193,217,177,114,194,218,178,115,192,216,179,258,264,263,257,23,186,124,204,21,187,125,205,188,123,206,22,189,19,120,207,190,20,121,208,191,18,122,209,184,14,130,210,131,185,12,211,183,13,129,212,180,17,126,213,181,15,127,214,182,16,128,215,261,271,272,262,164,28,101,243,162,29,99,244,27,100,245,163,24,167,97,242,25,165,98,240,26,166,96,241,34,159,107,247,105,35,160,248,33,161,106,249,30,158,103,250,31,156,104,246,32,157,102,251,267,270,269,268,155,76,139,85,153,77,140,86,75,138,84,154,72,151,142,88,73,152,143,89,74,150,141,87,82,146,137,91,135,83,144,92,81,145,136,90,78,149,133,94,79,147,134,95,80,148,132,93,256,255,253,252 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#dcedbe28d6e821630efaff61054e89b4af79513af364c6246d7e9f07a2213221, M = {0, 5, 10, 15, 20, 25, 30, 36, 40, 46, 51, 56, 60} 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 08:10:42 · history