Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma f23d34709f0d…

magma f23d34709f0d
Size
321
Isomorphism class hash
f23d34709f0d952e9e4aa963a8a0d757dd9469765fe380c57e73124c42f43c4f
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 22:22:12
Display reorder
300,3,201,141,59,43,41,202,4,142,60,42,203,2,143,61,39,6,200,140,58,7,40,198,138,56,38,5,199,139,57,9,192,49,132,50,10,193,47,133,51,8,194,48,134,52,195,12,45,135,53,136,196,13,46,54,197,11,44,137,55,309,301,303,305,95,291,288,290,289,293,295,96,292,294,296,299,97,297,298,284,94,287,285,286,92,277,279,276,278,281,93,283,280,282,86,255,252,253,254,87,259,256,257,258,88,263,261,260,262,267,89,264,265,266,269,271,90,268,270,275,91,272,273,274,320,318,319,317,32,243,25,165,242,246,247,33,23,166,250,251,34,24,167,238,35,239,21,164,36,124,234,22,162,125,37,235,20,163,30,231,128,16,156,31,232,126,14,157,29,233,127,15,158,230,26,131,19,159,17,228,27,129,160,229,28,130,18,161,313,314,307,312,71,153,209,107,225,226,154,72,207,108,227,155,73,208,109,224,70,152,205,106,68,222,150,206,104,223,69,151,204,105,62,144,216,215,98,63,145,217,213,99,64,146,218,214,100,147,65,219,211,101,212,148,66,220,102,149,67,221,210,103,306,310,304,302,74,174,180,240,241,244,175,75,181,245,248,176,76,182,249,236,77,177,183,237,78,116,178,184,1,117,79,179,185,0,80,172,113,186,120,81,173,114,187,118,82,171,115,188,119,168,83,112,189,123,190,169,84,110,121,170,85,111,191,122,311,315,316,308 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#1d08ed48a203bbb312f14b36e229a5f315d68c29c0949a9ef7235ea8d2bd9766, 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 22:22:13 · history