Equation 677 Database

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Magma 8223266785a4…

magma 8223266785a4
Size
595
Isomorphism class hash
8223266785a4d01ba2d87dcc59f057b7b22e882cce81d6191141ce03f9446df5
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
2026-10-08 16:54:47
Display reorder
38,43,39,40,41,42,60,65,61,62,63,64,335,334,333,331,332,330,298,297,299,294,295,296,479,478,477,474,476,475,530,533,520,567,555,258,257,161,255,256,200,199,160,157,158,159,156,113,112,114,109,110,111,68,67,69,224,223,66,238,237,183,184,90,91,165,164,166,167,168,266,208,267,209,268,206,207,220,178,221,176,222,177,185,94,95,96,92,93,414,416,415,417,418,419,497,496,495,494,493,492,463,462,464,466,467,465,385,384,386,388,389,387,502,501,503,498,499,500,328,327,329,324,325,326,392,391,390,393,394,395,540,546,534,536,527,535,532,579,565,548,592,587,556,572,566,588,13,12,14,15,16,17,33,32,35,36,37,34,122,121,123,124,125,126,142,141,143,144,145,146,3,2,4,5,0,1,28,27,29,30,31,215,234,83,235,236,181,182,228,227,70,225,226,179,189,133,134,135,131,132,451,450,452,454,455,453,446,445,444,449,447,448,471,473,472,469,468,470,438,440,439,441,442,443,365,364,363,361,362,360,433,432,434,435,436,437,504,509,506,508,505,507,539,528,514,522,512,513,547,583,557,562,549,550,558,575,578,573,147,152,148,149,150,151,74,73,76,71,72,75,7,6,8,9,10,11,88,87,89,84,85,86,100,99,101,102,103,98,105,108,106,107,104,274,280,169,281,277,272,273,275,278,163,279,276,265,233,82,78,79,80,81,378,380,379,381,382,383,312,314,313,315,316,317,408,410,409,411,412,413,289,288,290,292,293,291,283,284,282,287,285,286,398,397,396,400,401,399,407,406,405,402,403,404,538,542,515,511,523,521,518,564,570,594,571,559,591,551,561,584,21,26,22,23,24,25,153,249,197,248,198,250,174,173,219,175,218,172,214,170,171,18,19,20,51,50,52,53,216,217,97,240,239,187,186,269,211,271,213,270,210,212,259,202,260,203,261,201,180,232,229,77,230,231,346,345,347,343,344,342,356,355,354,359,357,358,481,482,480,483,484,485,322,321,323,319,320,318,309,311,310,308,306,307,337,336,338,339,340,341,303,305,304,301,302,300,541,545,531,529,525,524,526,552,553,593,569,585,589,568,560,563,57,56,58,59,54,55,155,252,254,154,251,253,191,190,244,242,136,243,245,192,193,137,138,139,129,128,130,127,188,241,247,246,194,195,196,140,117,116,118,119,120,115,44,49,45,46,47,48,162,205,262,263,264,204,375,377,376,372,373,374,349,348,350,352,353,351,421,420,422,424,425,423,456,458,457,459,460,461,487,488,486,491,489,490,426,428,427,431,429,430,368,367,366,369,370,371,537,543,517,519,510,516,544,581,577,574,582,586,576,580,590,554 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#40b1db721c17bf32e266eb97cd1492697125779c7804a195f580e3a793b1a85e, M = the submagma generated by {48, 60} (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 2026-10-08 16:54:48 · history