Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma d536f5f9dcb3…

magma d536f5f9dcb3
Size
321
Isomorphism class hash
d536f5f9dcb3b25ebefbc893f134af6c7a9a275d3c826949f9da35295ef39863
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 22:32:27
Display reorder
300,62,169,205,43,59,60,170,206,44,57,204,61,42,58,168,172,65,208,46,55,173,63,209,47,56,171,64,207,45,54,68,175,211,41,50,66,176,212,39,48,67,174,210,40,49,37,178,71,214,53,179,69,215,38,51,177,70,213,36,52,307,306,315,313,30,259,257,258,256,31,262,260,261,263,252,32,253,255,254,270,33,268,269,271,274,34,272,273,275,266,35,264,265,267,28,282,280,281,283,29,286,285,284,287,27,278,276,277,279,293,294,24,292,295,298,25,296,297,299,290,26,288,289,291,318,320,317,319,73,229,13,224,186,74,230,14,222,187,12,72,223,188,228,232,76,16,227,189,233,77,17,225,190,231,75,15,226,191,79,235,19,219,184,80,236,20,220,185,78,234,18,221,183,218,238,82,22,180,239,83,23,216,181,237,81,21,217,182,316,308,304,312,121,92,241,193,97,122,90,242,194,98,240,120,192,96,91,95,124,244,196,100,93,125,245,197,101,94,123,243,195,99,127,87,247,199,103,128,88,248,200,104,126,89,246,198,102,202,86,130,250,106,84,131,251,203,107,85,129,249,201,105,309,310,301,311,1,115,157,141,152,0,116,158,142,150,156,2,143,151,114,118,3,160,140,155,119,4,161,138,153,117,5,159,139,154,6,113,163,132,147,7,111,164,133,148,8,112,162,134,149,135,109,9,166,146,110,10,167,136,144,108,11,165,137,145,305,302,303,314 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#5779f8cee5daac7ffda88b67b379fba3aadfa70634d24364b86a2ac7cf85bc20, 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 22:32:28 · history