Equation 677 Database

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Magma 7e40c8a12481…

magma 7e40c8a12481
Size
595
Isomorphism class hash
7e40c8a12481d5d0763d70b8a9d9a591d2e64cf732216230cdc646576a08bb16
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 00:47:54
Display reorder
42,80,52,65,92,43,81,53,66,93,44,82,54,67,94,45,77,55,62,89,46,78,56,63,90,47,79,51,64,91,511,513,510,512,514,270,208,261,248,238,243,229,95,124,68,108,126,120,104,85,122,127,12,115,97,70,244,230,246,271,235,257,268,405,397,416,419,378,413,401,393,396,388,400,417,391,409,121,105,84,123,128,11,114,98,71,83,48,96,125,69,353,357,351,347,358,359,330,260,249,237,242,228,247,272,236,256,267,253,245,269,273,331,355,350,344,346,340,349,418,392,408,415,406,398,456,465,460,454,459,463,558,556,578,579,581,580,583,582,584,570,544,522,569,553,531,594,488,466,496,471,479,500,482,384,425,433,387,390,376,399,207,286,234,204,299,213,240,180,111,34,143,161,38,5,86,9,147,59,2,173,17,241,304,259,223,283,294,226,468,480,469,487,478,467,497,380,395,441,412,383,426,434,36,3,87,10,148,60,0,174,18,75,178,112,32,144,162,37,4,88,8,149,61,1,175,19,76,179,113,33,365,370,338,327,348,329,361,134,277,135,278,133,539,537,529,519,540,562,535,554,560,549,548,542,524,526,520,532,23,40,27,57,14,21,159,218,274,324,319,322,317,315,199,24,198,41,28,58,15,214,292,219,275,325,320,318,316,323,216,321,227,217,232,16,20,160,29,129,202,194,190,192,200,25,196,39,26,233,212,215,293,220,276,326,505,504,503,507,473,506,476,474,477,470,472,492,475,484,203,195,193,191,201,22,197,339,335,343,333,334,369,336,420,449,447,446,445,448,450,508,451,452,453,509,547,546,533,565,525,552,592,543,566,585,587,589,586,588,590,591,490,493,486,494,502,495,498,499,483,491,501,485,481,489,373,368,360,371,362,372,375,171,176,177,119,158,188,103,150,168,156,130,164,137,166,313,297,300,302,265,290,311,101,151,169,157,131,165,138,295,314,298,301,303,266,289,184,102,152,170,155,132,163,136,167,189,172,181,182,118,432,443,404,428,437,431,421,435,422,436,444,438,439,440,264,291,312,252,287,296,309,308,185,186,187,310,561,559,572,577,575,576,573,574,571,523,541,564,536,534,551,563,255,231,262,280,285,210,306,6,100,30,35,74,141,153,109,107,72,49,116,140,146,211,307,205,251,221,224,281,430,410,407,394,389,414,423,427,379,442,377,402,381,386,142,154,110,106,73,50,117,139,145,13,183,7,99,31,337,364,367,354,352,345,341,263,279,284,209,305,206,250,222,225,282,288,258,254,239,342,356,363,366,332,374,328,403,382,385,424,429,411,455,464,461,457,458,462,568,567,545,530,521,550,516,515,518,557,528,555,538,527,517,593 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#ab7663272fb322647e3a6f8af752cc36283f2dfca26817d870d65fdaf95a91e5, M = the submagma generated by {2, 7} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); 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: 85.

last edited by qawbecrdtey at 2026-10-07 00:47:55 · history