Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma c7b1494169a5…

magma c7b1494169a5
Size
321
Isomorphism class hash
c7b1494169a52a7dccaec6bee1935d6af68ae46e6fb0366fa732a4f4aa4fce9b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:32:46
Display reorder
300,50,21,37,53,7,38,48,54,8,19,36,20,49,55,6,52,39,23,211,230,196,51,22,56,250,238,210,207,57,5,41,45,16,58,12,42,46,17,59,13,40,47,18,60,11,44,43,15,61,9,231,229,14,62,10,63,240,239,206,205,314,311,315,302,281,282,175,280,283,176,285,284,287,286,174,278,276,277,279,292,178,294,293,295,179,297,298,296,299,177,288,290,289,291,181,273,274,272,275,182,264,266,265,267,180,268,270,269,271,256,184,258,257,259,260,185,262,261,263,253,252,183,254,255,318,319,317,320,201,151,4,199,221,204,246,244,116,152,3,150,133,125,220,223,1,154,127,118,0,135,155,128,119,2,134,153,126,117,33,132,149,124,64,34,130,147,122,65,35,131,148,123,66,129,32,145,222,212,200,195,146,121,67,120,245,237,225,213,305,306,309,307,169,94,73,27,190,74,170,28,191,92,72,93,168,29,189,172,76,97,26,193,77,173,95,24,194,75,171,96,25,192,71,167,90,209,188,215,165,217,30,228,70,166,91,31,187,203,69,197,236,234,249,214,241,208,251,235,164,68,89,186,316,313,301,312,111,140,82,102,159,83,112,103,160,141,81,139,110,101,158,114,78,143,105,162,79,115,144,106,163,80,113,142,104,161,87,109,138,100,157,88,108,137,98,156,86,219,224,99,227,198,84,233,218,248,243,216,247,232,226,242,107,85,136,202,310,303,308,304 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#58acf36cbe6044882516075a72a3c87dd19ad7333778c9b60a583a8d5c85fb41, M = {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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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 2026-10-01 22:32:47 · history