Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 51e7d0d7096c…

magma 51e7d0d7096c
Size
321
Isomorphism class hash
51e7d0d7096cd4c46d3ac281db0efc5d3f499338a3efdaf9ae24d9e568739eab
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 22:45:21
Display reorder
300,202,55,166,225,238,203,56,167,226,239,201,54,165,227,237,58,198,162,224,234,59,199,163,222,235,57,200,164,223,236,193,53,157,216,229,194,51,158,217,230,52,192,156,218,228,49,196,160,219,232,50,197,161,220,233,48,195,159,221,231,313,311,309,307,295,206,293,292,294,299,204,296,297,298,291,205,289,288,290,209,279,277,276,278,207,283,280,281,282,208,287,284,285,286,259,212,257,256,258,263,210,260,261,262,211,255,253,252,254,215,271,268,269,270,213,275,273,272,274,214,267,264,265,266,319,320,318,317,154,104,62,123,141,155,102,60,124,142,153,103,61,125,143,107,150,65,122,140,105,151,63,120,138,106,152,64,121,139,145,99,68,129,132,146,100,66,130,133,101,144,67,131,134,98,148,71,128,135,96,149,69,126,136,97,147,70,127,137,312,302,305,316,7,31,116,81,94,8,32,114,82,95,6,30,115,83,93,34,10,119,80,90,35,11,117,78,91,33,9,118,79,92,5,29,111,72,85,3,27,112,73,86,28,4,113,74,84,25,0,110,75,88,26,2,108,76,89,24,1,109,77,87,315,301,308,303,250,41,172,180,17,251,39,173,181,15,249,40,171,182,16,37,246,168,183,13,38,247,169,184,14,36,248,170,185,12,241,47,178,186,23,242,45,179,187,21,46,240,177,188,22,43,244,174,189,19,44,245,175,190,20,42,243,176,191,18,314,306,310,304 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#954a2425e38b1f8d73f83d01c811c18c22a6cf13713c169e64792ee66a752510, 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 22:45:22 · history