Equation 677 Database

← all  ·  ← by size  ·  ← size 451

Magma 1797d4f8e1f3…

magma 1797d4f8e1f3
Size
451
Isomorphism class hash
1797d4f8e1f389cb5d3354d5f2ec2ddc09513e5f78bb3995f26e007258757a99
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 450) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 14:39:55
Display reorder
449,446,448,447,442,440,445,441,444,443,450,311,239,227,189,85,177,47,325,339,150,240,312,220,190,86,178,40,326,340,151,313,241,221,191,87,179,41,327,341,152,314,242,222,192,88,172,42,328,342,153,307,243,223,193,89,173,43,329,343,154,155,236,308,224,194,90,174,44,330,344,148,237,309,225,195,91,175,45,323,345,238,149,310,226,188,92,176,46,324,351,1,0,14,28,10,11,7,22,375,374,376,373,372,379,380,381,377,378,384,385,386,383,382,389,390,391,387,388,395,394,396,393,392,399,400,401,397,398,405,404,406,403,402,409,410,411,407,408,415,414,416,413,412,419,420,421,417,418,428,424,425,426,423,422,429,430,431,427,358,354,355,356,353,352,359,360,361,357,364,368,365,366,363,362,369,370,371,367,434,439,435,437,438,432,433,436,62,212,130,286,104,73,253,48,272,306,213,63,131,287,105,74,254,49,273,299,64,214,124,288,106,75,255,50,274,300,65,215,125,289,107,76,256,51,267,301,66,216,126,290,108,77,257,52,268,302,303,217,68,127,283,101,70,258,67,269,304,218,60,128,284,102,71,252,39,270,219,305,61,129,285,103,72,350,346,271,12,13,16,30,18,24,29,20,335,233,181,316,122,167,144,82,35,207,234,336,182,317,123,168,145,83,36,208,337,235,183,318,116,169,146,84,37,209,338,228,184,319,117,170,147,78,38,210,331,229,185,320,118,171,140,79,32,211,204,230,332,186,321,119,164,141,80,69,205,231,333,187,322,120,165,142,81,33,232,206,334,180,315,121,166,143,348,34,2,3,4,6,15,21,26,5,160,265,246,291,133,280,58,99,114,197,266,161,247,292,134,281,59,100,115,198,162,259,248,293,135,282,53,93,109,199,163,260,249,294,136,275,54,94,110,200,156,261,250,295,137,276,55,95,111,201,202,262,157,251,296,138,277,56,96,112,203,263,158,244,297,139,278,57,97,113,264,196,159,245,298,132,279,347,98,349,9,8,17,31,19,23,27,25 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 451 = 11 + 5*88, 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#caa79eaa31d9024dd332fe8a59cc18f6143a257f1414b954b06eda001fed9cb8, M = {88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98} 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, 88): MacNeish's product over GF(8) x GF(11); GF(8) = F_2[x]/(x^3 + 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: 11.

last edited by qawbecrdtey at 2026-10-08 14:39:56 · history