Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma f58fd3e95bb5…

magma f58fd3e95bb5
Size
321
Isomorphism class hash
f58fd3e95bb51680db2ef6e8f63290ae0084310532a9a4ffda10a1cb3a40a02b
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 22:23:00
Display reorder
300,156,51,76,3,185,0,52,157,77,60,2,50,158,75,181,53,159,78,204,233,79,201,54,4,249,244,210,214,1,190,180,74,160,6,59,184,72,161,7,57,49,73,162,5,58,188,71,163,8,55,231,213,202,9,56,70,247,245,205,211,315,305,303,301,22,281,280,282,283,286,284,20,285,287,278,277,21,276,279,292,25,293,294,295,297,23,296,298,299,24,289,288,290,291,274,272,17,273,275,266,265,18,264,267,270,268,19,269,271,258,256,16,257,259,262,260,14,261,263,252,254,15,253,255,319,318,317,320,195,198,145,120,226,224,241,238,146,134,119,104,39,144,225,219,41,148,122,136,149,42,106,123,137,40,105,147,121,135,103,143,38,118,10,101,141,36,116,11,102,142,37,117,12,100,139,35,223,206,197,140,194,115,13,138,240,237,222,207,310,313,312,308,31,65,85,167,43,168,66,29,86,44,166,64,30,84,45,68,27,88,170,46,89,28,69,171,47,26,67,87,169,48,63,83,34,229,183,212,81,208,164,209,62,82,33,165,179,196,80,193,246,232,239,216,236,228,248,215,61,32,203,189,316,306,302,304,175,129,151,95,110,96,130,176,152,111,94,128,177,150,109,132,174,154,98,113,155,172,133,99,114,173,131,153,97,112,127,182,187,93,108,125,186,178,91,107,126,227,230,92,221,200,191,235,217,242,243,234,251,218,220,250,124,192,90,199,307,314,309,311 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#2c9cca33fbeafeb683cb8962a04870775a8e5c306e9c00d15364712f8c215d93, 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 22:23:01 · history