Equation 677 Database

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Magma 1c39eec93233…

magma 1c39eec93233
Size
595
Isomorphism class hash
1c39eec932330c651ed416b3d912f1f64e15dd5fca7fc39af4ea1de0176cd126
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
2026-10-06 10:53:57
Display reorder
89,4,74,161,162,90,5,75,157,85,0,76,158,86,1,77,159,87,2,78,160,88,3,79,53,55,56,51,52,54,510,561,517,516,512,238,209,235,315,273,296,259,46,146,70,188,101,44,201,144,197,59,198,11,57,195,274,297,260,234,286,247,314,407,392,457,430,398,455,377,397,453,420,440,410,395,432,71,189,102,45,203,145,60,199,12,58,194,129,168,106,338,356,342,368,350,336,371,322,237,320,208,236,316,272,298,261,233,287,246,326,324,337,374,373,340,369,328,339,452,419,439,409,394,431,401,463,459,393,465,461,585,580,524,532,564,539,541,528,520,545,534,588,593,590,549,538,478,469,484,474,471,503,505,448,418,438,383,408,416,412,224,204,241,205,218,251,225,29,171,182,179,127,166,26,104,121,109,34,64,6,22,252,226,221,302,309,308,271,502,470,489,493,491,473,479,376,382,405,388,386,443,449,181,128,167,23,105,122,110,35,65,7,20,91,36,28,170,183,180,126,165,24,103,119,108,32,63,8,21,92,334,333,363,366,365,353,362,25,258,120,264,33,578,575,527,565,566,571,522,572,530,514,515,559,531,513,574,511,149,9,95,186,141,115,134,239,222,268,242,289,262,255,97,13,147,14,10,93,187,284,266,281,240,223,269,243,290,263,254,256,288,210,206,94,185,140,116,132,62,31,118,66,150,107,96,98,148,211,207,253,313,285,267,282,477,472,492,480,499,490,486,488,498,467,466,485,507,497,114,133,61,30,117,67,151,351,347,348,357,329,327,346,450,428,414,424,399,387,415,481,433,411,406,487,591,592,579,537,535,586,550,546,552,553,526,583,521,529,548,581,483,482,500,506,475,495,509,501,468,496,494,508,476,504,335,358,345,359,343,361,367,43,131,196,164,15,137,125,193,50,173,39,82,152,72,292,311,230,278,317,294,213,138,123,192,47,174,40,83,291,248,293,310,231,279,318,163,16,139,124,190,48,172,41,84,153,73,156,184,42,423,454,437,378,427,417,451,396,444,391,404,434,402,436,312,232,280,319,295,212,283,270,191,49,175,229,582,584,587,563,544,562,540,589,560,518,542,573,569,556,570,557,245,250,215,228,275,299,304,19,27,177,99,154,135,200,143,111,68,112,81,18,38,276,300,305,216,219,307,257,435,425,456,429,400,413,403,379,390,422,441,446,380,384,178,100,155,136,202,142,69,113,80,17,37,130,169,176,331,332,364,349,360,354,370,321,244,265,249,214,227,277,301,303,217,220,306,323,325,355,375,372,341,352,344,330,389,421,442,445,381,385,447,458,462,426,464,460,525,536,558,568,576,555,543,567,577,519,554,523,594,533,547,551 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 {16, 17} (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 2026-10-06 10:53:58 · history