Equation 677 Database

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Magma 0c05ad6be1e0…

magma 0c05ad6be1e0
Size
321
Isomorphism class hash
0c05ad6be1e0b6dbda8e9c119f6ebbeb002cec75c3b0b3906a8a25d6d640237f
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 22:27:05
Display reorder
300,18,62,203,126,0,19,60,127,204,2,17,61,125,202,1,58,16,128,206,4,59,9,129,207,5,57,224,231,205,3,11,209,68,131,7,12,210,66,132,8,10,208,67,130,6,212,14,64,133,20,213,15,65,134,21,211,13,63,232,225,315,308,301,313,257,246,258,259,256,260,247,262,261,263,252,248,254,253,255,249,268,270,269,271,250,272,274,273,275,251,265,266,264,267,280,281,244,282,283,284,285,245,286,287,276,277,243,278,279,293,292,240,294,295,297,296,241,298,299,288,289,242,290,291,319,320,317,318,138,51,34,147,227,233,52,148,35,97,139,53,146,33,96,54,137,150,37,93,55,135,151,38,94,56,136,149,36,95,143,40,49,153,101,144,41,50,154,102,145,39,48,152,100,43,142,45,155,98,44,140,46,156,99,42,141,47,234,228,305,310,303,302,107,76,177,158,32,108,77,159,178,30,106,75,157,176,31,79,103,161,173,28,80,104,162,174,29,78,105,160,175,27,112,169,74,164,24,113,170,72,165,22,111,168,73,163,23,171,109,70,167,226,172,229,71,235,25,236,110,69,166,26,309,311,316,306,192,86,182,219,115,193,84,217,183,116,191,85,218,184,114,82,195,215,181,118,83,196,216,179,119,81,194,214,180,117,198,188,92,223,121,199,189,90,221,122,197,190,91,222,120,187,201,88,239,124,185,237,89,238,230,186,200,87,220,123,304,312,307,314 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#33430dadf8546adceaddacfc75eeb6c00258f5413ce1926e16e948db7c79b4f3, 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 22:27:06 · history