Equation 677 Database

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Magma 83bc09016c0f…

magma 83bc09016c0f
Size
705
Isomorphism class hash
83bc09016c0fc6f72b0e34891c768080e13c908dfaa33d43e27770aa48aa9ede
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 17:18:34
Display reorder
660,290,587,325,314,302,288,585,326,312,300,289,586,324,313,301,583,293,328,317,305,584,291,329,315,303,582,292,327,316,304,331,296,578,320,308,332,294,576,318,306,330,295,577,319,307,299,334,581,323,311,297,335,579,321,309,298,333,580,322,310,687,688,686,685,372,237,362,396,386,373,238,360,397,384,374,239,361,398,385,236,375,365,399,389,234,376,363,400,387,235,377,364,401,388,368,378,228,402,392,366,379,229,403,390,367,380,230,404,391,381,371,231,405,395,382,369,232,406,393,383,370,233,407,394,703,704,701,702,562,279,544,531,568,563,280,545,532,569,561,281,543,533,567,278,558,540,530,564,276,559,541,528,565,277,560,542,529,566,550,553,285,537,574,551,554,286,538,575,549,552,287,539,573,556,546,284,536,570,557,547,282,534,571,555,548,283,535,572,671,672,670,669,251,18,416,75,263,249,19,414,76,261,250,20,415,77,262,21,247,419,74,259,22,248,417,72,260,23,246,418,73,258,411,242,16,81,254,412,240,17,82,252,413,241,15,83,253,245,410,12,80,257,243,408,13,78,255,244,409,14,79,256,679,680,678,677,91,28,441,428,96,92,29,442,426,97,90,27,443,427,98,24,94,440,431,99,25,95,438,429,100,26,93,439,430,101,432,89,34,423,102,433,87,35,424,103,434,88,33,425,104,85,435,30,422,105,86,436,31,420,106,84,437,32,421,107,692,691,690,689,10,114,178,164,498,11,115,179,162,499,9,116,177,163,500,117,6,174,167,501,118,7,175,165,502,119,8,176,166,503,169,0,112,159,496,170,2,113,160,497,168,1,111,161,495,4,172,108,158,492,5,173,109,156,493,3,171,110,157,494,699,700,698,697,127,210,36,60,48,128,211,37,61,49,126,212,38,62,50,213,130,39,63,51,214,131,40,64,52,215,129,41,65,53,42,125,208,66,54,43,123,209,67,55,44,124,207,68,56,121,45,204,69,57,122,46,205,70,58,120,47,206,71,59,663,664,662,661,595,338,626,614,602,596,336,624,612,600,594,337,625,613,601,341,598,629,617,605,339,599,627,615,603,340,597,628,616,604,632,593,344,620,608,630,591,342,618,606,631,592,343,619,607,589,635,347,623,611,590,633,345,621,609,588,634,346,622,610,682,683,684,681,650,182,649,648,651,654,180,653,652,655,658,181,657,656,659,185,646,644,645,647,183,638,637,636,639,184,642,641,640,643,510,518,188,508,525,511,516,186,509,526,512,517,187,507,527,521,513,191,504,524,519,514,189,505,522,520,515,190,506,523,695,696,693,694,449,267,484,473,461,447,268,485,471,459,448,269,483,472,460,266,445,480,469,457,264,446,481,470,458,265,444,482,468,456,490,455,273,479,467,491,453,274,477,465,489,454,275,478,466,451,486,272,475,463,452,487,270,476,464,450,488,271,474,462,667,668,665,666,139,219,197,356,145,140,220,195,354,146,138,221,196,355,144,218,142,193,359,148,216,143,194,357,149,217,141,192,358,147,203,137,225,351,151,201,135,226,352,152,202,136,227,353,150,133,199,224,350,154,134,200,222,348,155,132,198,223,349,153,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#4dbd6b0006d3996c22611f6a9a74b6d8666415e8467cb95ff3380ed5b17e9234, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 17:18:36 · history