Equation 677 Database

← all  ·  ← by size  ·  ← size 409

Magma 169a6c4f0304…

magma 169a6c4f0304
Size
409
Isomorphism class hash
169a6c4f0304fd4ccb9dd804567c036a9bdbc44cb4d6ed1293990c9883595342
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 358 (nullity 51) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 05:43:42
Display reorder
407,403,404,405,406,401,402,400,408,347,20,22,348,372,45,47,373,197,70,72,198,222,93,95,223,244,118,120,249,269,143,145,274,297,168,170,298,73,71,74,196,195,96,94,220,97,221,121,119,242,122,243,146,144,267,147,268,171,169,295,172,296,396,394,320,397,321,21,23,345,24,346,370,48,46,49,371,322,393,395,323,324,270,299,374,199,224,245,349,327,16,3,330,352,41,28,355,177,50,54,180,203,98,78,206,226,123,103,246,259,148,128,272,276,173,153,280,52,51,53,175,179,76,75,205,77,200,101,100,229,102,225,126,125,258,127,250,150,151,279,152,277,376,375,304,377,302,0,1,329,2,325,354,25,26,27,351,300,399,378,305,303,251,278,353,178,204,228,328,339,11,13,335,364,36,38,360,189,62,64,185,215,86,88,211,237,111,113,233,257,136,138,256,289,161,163,285,60,63,61,188,187,84,87,213,85,214,109,112,235,110,236,134,137,263,135,264,159,162,287,160,288,384,387,312,385,313,12,9,337,10,338,362,34,37,35,363,314,386,388,310,311,262,286,361,186,212,234,336,341,19,15,342,366,44,40,367,191,69,66,192,201,92,99,217,248,117,124,239,273,142,149,253,291,167,174,292,67,65,68,190,194,90,89,219,91,216,115,114,241,116,238,140,139,266,141,265,165,164,294,166,290,390,389,319,391,315,14,17,344,18,340,369,42,39,43,365,316,392,398,317,318,254,293,368,193,218,240,343,334,6,8,326,359,31,33,350,184,57,59,176,210,81,83,202,227,106,108,247,255,131,133,271,284,156,158,275,55,58,56,183,182,79,82,208,80,209,104,107,231,105,232,129,132,260,130,261,154,157,282,155,283,379,382,307,380,308,7,4,332,5,333,357,29,32,30,358,309,381,383,301,306,252,281,356,181,207,230,331 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 409 = 9 + 5*80, 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#1c1045d74cc5a6cd35415a2d56a5971c4505b0d3fed33db6316f8fcb706a4e5f, M = {0, 5, 10, 15, 20, 25, 30, 75, 88} 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, 80): MacNeish's product over GF(16) x GF(5); GF(16) = F_2[x]/(x^4 + 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: 1.

last edited by qawbecrdtey at 2026-10-07 05:43:43 · history