Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 144bb9ba6fea…

magma 144bb9ba6fea
Size
321
Isomorphism class hash
144bb9ba6feab999b2106dc8da757be89596352c32a5a676b21fefa04d2349ec
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 22:32:15
Display reorder
300,114,149,219,157,99,115,147,220,158,100,116,148,221,156,101,117,145,218,160,98,118,146,216,161,96,119,144,217,159,97,225,112,155,163,105,226,113,153,164,106,227,111,154,162,107,108,224,151,166,104,109,222,152,167,102,110,223,150,165,103,316,315,302,301,264,265,41,266,267,269,268,39,270,271,273,272,40,274,275,261,260,37,262,263,253,252,38,254,255,257,256,36,258,259,47,288,289,291,290,45,293,292,295,294,46,297,296,298,299,285,43,284,287,286,276,44,277,279,278,281,42,280,283,282,319,320,318,317,235,234,55,124,177,237,236,56,125,178,239,238,54,123,179,232,233,58,120,176,228,229,59,121,174,230,231,57,122,175,53,246,247,130,168,51,248,249,131,169,52,250,251,129,170,244,49,245,126,171,240,50,241,127,172,242,48,243,128,173,309,310,308,307,63,14,31,183,201,64,12,32,184,202,65,13,30,185,203,62,17,34,182,200,60,15,35,180,198,61,16,33,181,199,29,69,20,189,192,27,70,18,190,193,28,71,19,191,194,68,25,23,188,195,66,26,21,186,196,67,24,22,187,197,312,311,303,306,81,7,204,135,93,82,8,205,136,94,83,6,206,137,95,80,10,207,134,92,78,11,208,132,90,79,9,209,133,91,210,72,5,141,84,211,73,3,142,85,212,74,4,143,86,75,213,0,140,87,76,214,2,138,88,77,215,1,139,89,313,314,305,304 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#555d8536a50144822bfea9b20f3ef68710f5792b887e6dda4840627962426043, 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 22:32:21 · history