Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma fddeccecaed9…

magma fddeccecaed9
Size
321
Isomorphism class hash
fddeccecaed986e77e3765ddde3e0b000d02513d60cd4031b368b44c5893e03c
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 22:45:57
Display reorder
300,123,80,217,243,231,124,78,244,218,232,245,79,125,216,233,83,122,220,242,230,81,120,221,240,228,82,121,219,241,229,129,75,223,249,237,130,76,224,250,238,131,77,222,251,239,128,74,226,248,236,126,72,227,246,234,127,73,225,247,235,311,315,303,304,265,3,264,266,267,269,4,270,268,271,274,5,272,273,275,2,261,260,262,263,1,253,252,254,255,0,257,256,258,259,289,9,288,291,290,292,10,293,295,294,296,11,297,299,298,284,8,285,286,287,277,6,276,278,279,280,7,281,282,283,317,319,318,320,94,59,69,171,161,95,57,172,70,159,173,58,93,71,160,55,90,68,170,157,56,91,66,168,158,54,92,67,169,156,85,50,60,177,167,86,48,61,178,165,84,49,62,179,166,88,53,63,176,163,89,51,64,174,164,87,52,65,175,162,314,306,302,316,195,47,139,181,106,196,45,182,140,107,180,46,197,138,105,43,194,142,184,102,44,192,143,185,103,42,193,141,183,104,201,38,137,187,97,202,36,135,188,98,203,37,136,186,96,200,41,133,190,100,198,39,134,191,101,199,40,132,189,99,313,301,310,307,207,109,147,24,19,208,110,25,148,20,26,108,209,149,18,112,206,146,27,22,113,204,144,28,23,111,205,145,29,21,213,115,153,30,17,214,116,154,31,15,215,114,155,32,16,212,118,152,33,13,210,119,150,34,14,211,117,151,35,12,312,309,305,308 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#9f23da9903d6ebc1c6f98cbe23264669be86f8e7144737b42fbccbf8aeddcd62, 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 22:45:58 · history