Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 627e4e1a96e6…

magma 627e4e1a96e6
Size
321
Isomorphism class hash
627e4e1a96e6ca1fa87cf0222e0511226b458092ba42a7e0ad7a52a223a91abd
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 22:37:30
Display reorder
300,87,169,37,110,125,88,38,111,126,170,86,171,36,112,127,33,90,168,113,124,91,34,166,114,122,89,35,167,115,123,108,85,43,160,116,83,44,161,109,117,84,42,162,107,118,39,81,163,104,119,40,82,164,105,120,41,80,165,106,121,301,302,303,310,154,289,290,291,288,155,294,295,292,293,156,297,298,299,296,286,157,284,287,285,158,278,277,279,276,159,282,281,283,280,255,152,254,252,253,153,258,256,259,257,151,262,261,263,260,266,148,264,267,265,270,149,268,271,269,274,150,272,275,273,319,317,318,320,50,205,217,147,134,48,218,246,247,206,49,207,219,251,250,216,46,204,146,135,47,214,202,144,136,45,215,203,145,137,138,56,208,196,132,54,209,197,139,133,55,210,198,140,131,211,52,199,141,128,212,53,200,142,129,213,51,201,143,130,313,315,307,309,2,226,241,181,190,1,242,182,191,227,0,228,243,183,192,240,5,229,180,193,3,238,230,178,194,4,239,231,179,195,172,8,232,224,188,6,233,225,173,189,7,234,223,174,187,235,11,220,175,184,236,9,221,176,185,237,10,222,177,186,304,305,306,312,94,20,69,64,73,92,245,65,244,18,93,19,248,63,249,70,97,23,67,24,95,71,21,68,25,96,72,22,66,26,62,100,78,15,27,98,79,16,60,28,99,77,17,61,29,74,103,14,58,30,75,101,12,59,31,76,102,13,57,32,316,308,311,314 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#6f4d58a1f1a96be51a4fbe5ecc6c97c30dc38acf270b654112619a91916a19da, 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 22:37:31 · history