Equation 677 Database

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Magma cd8515053628…

magma cd8515053628
Size
705
Isomorphism class hash
cd85150536289011c8387e6d08a00f88b5f7aeb3b9ed04c6f359d0b3967139b4
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 20:36:12
Display reorder
660,342,364,143,377,380,343,365,375,141,378,344,363,142,376,379,360,345,139,373,383,361,346,140,374,381,362,347,138,372,382,355,348,149,368,386,356,349,147,366,384,354,350,148,367,385,351,358,145,371,389,352,359,146,369,387,353,357,144,370,388,685,686,688,687,228,237,459,181,187,229,238,182,460,188,230,239,461,180,186,236,231,458,184,190,234,232,456,185,191,235,233,457,183,189,243,226,450,179,193,244,227,451,177,194,245,225,452,178,192,222,242,453,175,196,223,240,454,176,197,224,241,455,174,195,701,702,704,703,569,579,333,599,558,567,580,597,334,559,568,581,335,598,560,578,565,332,595,561,576,566,330,596,562,577,564,331,594,563,585,575,339,590,556,586,573,340,588,557,587,574,341,589,555,571,584,338,593,552,572,582,336,591,553,570,583,337,592,554,670,669,672,671,468,248,42,261,280,469,246,262,43,281,470,247,44,263,279,251,471,45,260,276,249,472,46,258,277,250,473,47,259,278,254,466,48,267,271,252,467,49,268,272,253,465,50,269,270,462,257,51,266,274,463,255,52,264,275,464,256,53,265,273,680,677,679,678,498,519,58,477,497,499,520,478,59,495,500,521,57,479,496,518,501,54,476,493,516,502,55,474,494,517,503,56,475,492,510,504,64,483,488,511,505,65,484,486,512,506,63,485,487,507,513,60,482,491,508,514,61,480,489,509,515,62,481,490,689,690,691,692,300,311,102,26,542,301,309,24,103,540,302,310,104,25,541,307,303,105,29,545,308,304,106,27,543,306,305,107,28,544,317,298,108,32,537,315,299,109,30,538,316,297,110,31,539,294,313,111,35,536,295,314,112,33,534,296,312,113,34,535,697,698,700,699,89,69,635,606,615,87,70,607,633,616,88,71,634,608,617,68,85,631,609,614,66,86,632,610,612,67,84,630,611,613,75,80,626,604,621,76,78,624,605,622,77,79,625,603,623,83,74,629,600,620,81,72,627,601,618,82,73,628,602,619,661,662,664,663,407,417,161,435,395,405,418,436,159,393,406,419,160,437,394,416,403,157,434,391,414,404,158,432,392,415,402,156,433,390,423,413,152,426,401,424,411,150,427,399,425,412,151,428,400,409,422,155,429,397,410,420,153,430,398,408,421,154,431,396,682,681,684,683,125,118,326,548,37,123,119,546,324,38,124,117,325,547,36,114,121,329,551,40,115,122,327,549,41,116,120,328,550,39,640,642,321,643,641,646,644,322,647,645,636,637,323,638,639,654,652,320,655,653,658,656,318,659,657,650,649,319,651,648,693,694,696,695,90,9,524,12,290,91,10,13,522,288,92,11,523,14,289,8,93,527,15,293,6,94,525,16,291,7,95,526,17,292,1,96,530,18,285,0,97,528,19,286,2,98,529,20,287,99,3,533,21,284,100,4,531,22,282,101,5,532,23,283,666,665,668,667,211,168,449,134,205,212,169,132,447,206,210,170,448,133,204,171,214,445,137,208,172,215,446,135,209,173,213,444,136,207,166,217,440,129,203,167,218,438,130,201,165,216,439,131,202,220,162,443,128,199,221,163,441,126,200,219,164,442,127,198,674,673,676,675 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#c6a869941d5f836cd5f826f4a41a523fb37d651c2417bcc51f4579b275cefef3, 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 20:36:13 · history