Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 4b8c4aba3d8a…

magma 4b8c4aba3d8a
Size
321
Isomorphism class hash
4b8c4aba3d8ab747f39783aecb257a02f9e7f4fa7d9ff0c036474a225d8c0dd5
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 23:03:43
Display reorder
300,84,148,238,184,244,85,149,185,239,245,147,183,86,237,243,87,144,180,234,240,88,145,181,235,241,89,146,182,236,242,154,229,90,190,250,155,230,91,191,251,153,228,92,189,249,150,232,93,186,246,233,151,94,187,247,152,231,95,188,248,303,305,315,311,19,268,271,269,270,20,272,273,275,274,264,265,18,266,267,22,252,253,255,254,23,256,257,259,258,21,260,261,262,263,293,295,17,292,294,296,298,15,297,299,289,290,16,288,291,277,279,13,276,278,283,281,14,280,282,284,287,12,285,286,318,320,319,317,50,102,39,220,114,48,103,221,40,115,104,219,49,41,116,53,105,216,38,117,51,106,217,36,118,52,107,218,37,119,100,45,56,226,112,101,46,54,227,113,99,47,55,225,111,96,44,59,222,108,42,97,57,223,109,98,43,58,224,110,316,308,302,312,69,1,130,29,196,70,0,27,131,197,2,28,71,129,195,68,3,25,126,192,66,4,26,127,193,67,5,24,128,194,6,121,60,35,202,7,122,61,33,203,8,120,62,34,201,9,124,63,31,198,125,10,64,32,199,11,123,65,30,200,301,310,306,313,72,133,208,170,159,73,134,168,209,160,132,169,74,207,161,75,136,173,204,158,76,137,171,205,156,77,135,172,206,157,139,214,78,176,165,140,215,79,174,166,138,213,80,175,167,142,210,81,179,164,211,143,82,177,162,141,212,83,178,163,307,304,309,314 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#f1e2c600ebf06c2e31b8968226514217c5fc265d2577d787fe558118ce3f2b96, 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 23:03:44 · history