Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma d81d704cb9ea…

magma d81d704cb9ea
Size
321
Isomorphism class hash
d81d704cb9eab1cc102dcd5b0a3af8ad926720205d5c288e7a58b8f26f5e6547
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 22:32:43
Display reorder
300,214,112,48,170,88,212,110,49,168,86,213,111,47,169,87,115,217,44,173,91,113,215,45,171,89,114,216,46,172,90,118,220,176,39,94,116,218,174,40,92,117,219,175,38,93,223,121,179,42,97,221,119,177,43,95,222,120,178,41,96,303,305,311,306,263,262,261,244,260,254,253,252,245,255,258,257,256,243,259,273,274,272,240,275,265,266,264,241,267,269,270,268,242,271,284,286,250,285,287,277,278,251,276,279,280,282,249,281,283,298,296,246,297,299,290,289,247,288,291,294,293,248,292,295,319,318,320,317,73,136,184,54,163,71,134,182,55,161,72,135,183,53,162,139,69,187,50,159,137,70,185,51,160,138,68,186,52,158,142,64,60,226,224,140,62,61,180,164,141,63,59,181,165,67,145,56,239,236,65,143,57,231,229,66,144,58,235,232,315,313,301,307,132,148,84,19,103,133,146,85,17,101,131,147,83,18,102,151,128,80,15,99,149,129,81,16,100,150,130,82,14,98,154,123,25,75,109,152,124,23,76,107,153,122,24,74,108,126,157,21,78,105,127,155,22,79,106,125,156,20,77,104,312,302,304,308,195,6,11,27,202,196,7,12,28,200,194,5,13,26,201,2,198,10,30,205,3,199,8,31,203,4,197,9,29,204,227,193,33,225,208,0,191,34,166,206,1,192,32,167,207,189,237,36,238,211,190,228,37,230,209,188,233,35,234,210,314,310,309,316 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#58758ff0293182d6dd53be73984d3e209a66569482d3b8502bf477ddaee58f10, 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 22:32:44 · history