Equation 677 Database

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Magma 5c36830cfede…

magma 5c36830cfede
Size
707
Isomorphism class hash
5c36830cfedec361136020b0b53146398560f95df4ed9810ee10c80573fb8a29
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 11:14:51
Display reorder
300,301,302,305,303,304,656,101,100,96,97,98,99,108,110,109,112,113,111,124,123,125,122,120,121,134,133,132,137,135,136,209,208,207,204,205,206,94,93,95,92,90,91,63,65,64,60,61,62,1,2,0,3,4,5,31,30,32,33,34,35,160,159,161,157,158,156,320,319,321,322,323,318,346,345,347,342,343,344,595,599,594,596,597,598,496,495,497,492,493,494,590,588,591,592,593,589,460,459,461,456,457,458,469,468,470,471,472,473,316,315,317,312,313,314,398,397,399,400,401,396,585,584,586,587,582,583,614,616,606,623,609,624,628,633,625,649,675,693,678,664,666,665,662,667,663,661,144,146,148,149,147,145,270,271,272,275,273,274,248,246,247,249,250,251,265,266,264,267,268,269,77,76,75,72,73,74,42,44,43,46,47,45,214,213,215,210,212,211,128,127,126,131,129,130,119,118,117,115,116,114,261,263,262,259,258,260,425,424,420,421,422,423,601,605,600,602,603,604,525,524,526,527,522,523,382,381,383,378,379,380,518,517,519,520,521,516,392,391,393,394,395,390,389,388,384,385,386,387,329,328,324,325,326,327,368,367,369,370,371,366,331,330,332,333,334,335,648,651,639,642,629,652,634,635,626,644,694,696,673,660,676,670,671,659,668,677,23,22,18,19,20,21,104,103,102,105,106,107,80,79,78,81,82,83,153,155,154,150,151,152,142,141,143,140,138,139,297,295,296,298,299,288,234,235,236,238,239,237,255,257,256,253,252,254,243,245,244,242,241,240,38,37,36,41,39,40,500,499,501,502,503,498,474,479,475,476,477,478,440,439,441,442,443,438,431,430,426,427,428,429,452,451,453,454,455,450,435,434,436,437,432,433,359,358,354,355,356,357,418,417,419,414,415,416,403,402,404,405,406,407,580,579,581,576,577,578,645,650,637,647,627,646,621,638,622,640,697,698,669,690,691,689,687,688,692,695,201,203,199,200,198,202,184,183,185,182,180,181,278,276,277,279,280,281,188,187,186,191,189,190,167,166,165,162,163,164,291,290,289,292,293,294,173,172,171,170,168,169,176,175,174,179,177,178,197,196,195,193,194,192,285,287,286,283,282,284,542,541,543,544,545,540,565,564,566,567,568,569,552,557,553,554,555,556,365,364,360,361,362,363,547,546,548,549,550,551,559,558,560,561,562,563,530,529,531,532,533,528,376,375,377,372,373,374,538,537,539,534,535,536,575,574,570,571,572,573,655,654,631,643,632,653,617,630,618,641,674,699,672,701,704,700,703,702,705,706,16,15,14,12,13,17,229,228,230,233,231,232,221,220,219,216,217,218,66,68,67,69,70,71,87,89,88,85,86,84,223,222,224,227,225,226,27,29,28,24,25,26,48,49,50,52,53,51,57,59,58,56,55,54,6,8,7,9,10,11,444,449,445,446,447,448,351,350,352,353,348,349,336,341,337,338,339,340,466,465,467,462,463,464,308,306,309,310,311,307,488,487,489,490,491,486,485,484,480,481,482,483,505,504,506,507,508,509,514,513,515,510,511,512,409,408,410,411,412,413,619,613,607,612,608,620,610,615,611,636,679,658,657,685,681,686,683,680,682,684 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#ca4e87f44b5aa8ee937e3111d7e18929d38c701d18b6266af0f19751e7c29bcd, M = {36, 37, 38, 39, 40, 41, 136} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-06 11:14:52 · history