Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 2c233277352f…

magma 2c233277352f
Size
321
Isomorphism class hash
2c233277352f10aea57723f0831ed471d6ff975cac9c8379b65e93461b84ddc9
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 23:04:12
Display reorder
300,280,279,281,278,276,277,285,286,287,284,282,283,136,137,135,132,133,134,142,143,141,138,139,140,16,17,15,12,13,14,22,23,21,18,19,20,190,191,189,186,187,188,181,182,180,184,185,183,236,234,235,239,237,238,231,232,233,230,228,229,302,305,311,316,79,78,80,81,82,83,76,77,75,72,73,74,41,39,40,37,38,36,47,45,46,43,44,42,54,55,56,57,58,59,52,53,51,48,49,50,68,66,67,71,69,70,63,64,65,62,60,61,85,86,84,88,89,87,91,92,90,94,95,93,317,318,319,320,150,152,151,155,153,154,147,148,149,146,144,145,199,200,198,202,203,201,197,195,196,193,194,192,295,296,294,298,299,297,293,291,292,289,290,288,247,248,246,250,251,249,245,243,244,241,242,240,160,161,159,156,157,158,166,167,165,162,163,164,303,312,310,315,99,101,100,97,98,96,107,105,106,103,104,102,168,169,170,171,172,173,174,175,176,177,178,179,3,4,5,2,1,0,9,10,11,8,6,7,252,253,254,255,256,257,258,259,260,261,262,263,209,207,208,205,206,204,215,213,214,211,212,210,304,306,309,314,123,125,124,121,122,120,131,129,130,127,128,126,116,114,115,119,117,118,111,112,113,110,108,109,24,25,26,27,28,29,30,31,32,33,34,35,224,222,223,227,225,226,219,220,221,218,216,217,265,266,264,268,269,267,271,272,270,274,275,273,301,307,308,313 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {64} 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 23:04:13 · history