Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 0fd3d175fb79…

magma 0fd3d175fb79
Size
321
Isomorphism class hash
0fd3d175fb7955ea6b90f27d2ffb9bb2a4fc288c4dc4e9f5da8b0a6afdc37bde
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 22:22:49
Display reorder
300,216,243,5,147,231,217,244,148,3,232,218,245,4,149,233,242,219,0,146,230,240,220,2,144,228,241,221,1,145,229,249,153,222,11,237,250,154,223,9,238,251,155,224,10,239,152,248,225,7,236,150,246,226,8,234,151,247,227,6,235,313,307,311,306,265,264,30,267,266,269,268,271,31,270,272,273,32,275,274,260,261,33,263,262,252,253,34,255,254,256,257,35,259,258,289,290,288,28,291,293,294,292,29,295,296,298,297,27,299,286,284,285,24,287,278,277,276,25,279,282,280,281,26,283,320,317,319,318,203,170,20,184,206,201,168,185,18,204,202,169,19,183,205,173,199,23,180,209,171,200,21,181,207,172,198,22,182,208,176,190,194,15,212,174,191,192,16,210,175,189,193,17,211,186,179,197,14,215,187,177,195,12,213,188,178,196,13,214,316,305,310,308,70,45,167,58,81,71,46,59,165,82,69,47,166,57,83,44,66,163,54,80,42,67,164,55,78,43,68,162,56,79,36,49,61,158,72,37,50,62,156,73,38,48,60,157,74,52,39,64,161,75,53,40,65,159,76,51,41,63,160,77,315,301,309,302,109,85,133,97,121,110,86,98,134,122,108,84,132,96,120,88,112,136,100,124,89,113,137,101,125,87,111,135,99,123,91,103,115,139,127,92,104,116,140,128,90,102,114,138,126,106,94,118,142,130,107,95,119,143,131,105,93,117,141,129,314,304,312,303 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#25532901b7174194dca0f8f453aa2ae473cc5b2aa34d04b35f0c3beb206af29c, 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 22:22:50 · history