Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 2fa59078aba4…

magma 2fa59078aba4
Size
321
Isomorphism class hash
2fa59078aba4bbecefb9fe6fe11eb452ae8e3469998fdd334f98e1abca520010
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 22:37:45
Display reorder
300,182,62,178,99,161,60,159,180,179,100,61,160,181,177,101,185,157,65,174,98,183,158,63,175,96,184,156,64,176,97,167,68,169,188,105,165,66,170,186,106,166,67,168,187,107,163,71,172,191,104,189,164,69,173,102,162,70,171,190,103,308,311,307,303,262,244,261,263,260,245,255,253,252,254,243,259,257,256,258,273,275,240,272,274,264,267,241,265,266,269,271,242,268,270,287,250,285,284,286,279,251,276,277,278,283,249,281,280,282,299,246,297,296,298,289,291,247,288,290,295,248,292,293,294,318,317,320,319,81,51,12,89,24,52,25,82,13,87,53,26,83,14,88,80,27,50,15,85,78,28,48,16,86,79,29,49,17,84,30,57,18,72,95,31,58,19,73,93,32,59,20,74,94,33,56,21,75,91,76,34,54,22,92,35,55,23,77,90,316,315,302,301,126,11,194,137,118,9,119,127,192,135,10,117,128,193,136,129,114,7,197,133,130,115,8,195,134,131,116,6,196,132,109,2,200,124,143,110,1,198,125,141,108,0,199,123,142,112,5,203,120,139,121,113,3,201,140,111,4,202,122,138,304,305,309,312,38,216,146,217,209,218,207,36,144,219,220,208,37,145,221,41,205,223,149,222,39,206,225,147,224,40,204,226,148,227,215,229,152,44,228,213,231,150,42,230,214,233,151,43,232,211,235,155,47,234,45,212,236,153,237,210,238,154,46,239,306,313,314,310 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#789271f8e1620c5f8875a1b32dfd6da1b71c443ca3fc9082ace33bb0fcd8a22c, 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 22:37:46 · history