Equation 677 Database

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Magma 40696abf009c…

magma 40696abf009c
Size
705
Isomorphism class hash
40696abf009c8daf60e794b7c1035d161e5a92b8e725af831b09300765194037
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 19:51:39
Display reorder
660,556,568,544,581,63,557,64,569,545,579,555,65,567,543,580,62,552,564,540,577,60,553,565,541,578,61,554,566,542,576,574,562,69,550,587,575,563,70,551,585,549,573,561,71,586,558,570,68,546,583,559,571,66,547,584,560,572,67,548,582,687,688,686,685,270,279,320,241,8,271,6,280,318,242,272,7,281,319,240,11,273,278,323,244,9,274,276,321,245,10,275,277,322,243,285,268,3,315,247,286,269,4,316,248,317,287,267,5,246,264,284,2,314,250,265,282,1,312,251,266,283,0,313,249,703,704,701,702,506,526,497,539,218,504,216,527,495,537,505,217,525,496,538,221,509,522,493,535,219,507,523,494,536,220,508,524,492,534,517,512,224,503,530,518,510,222,501,528,502,516,511,223,529,515,520,227,499,533,513,521,225,500,531,514,519,226,498,532,671,672,670,669,336,348,331,362,26,337,24,349,332,360,338,25,350,330,361,29,339,351,334,365,27,340,352,335,363,28,341,353,333,364,354,342,32,329,368,355,343,30,327,366,328,356,344,31,367,345,357,35,325,371,346,358,33,326,369,347,359,34,324,370,679,680,678,677,155,160,135,171,372,153,373,161,136,172,154,374,159,137,173,375,151,156,134,170,376,152,157,132,168,377,150,158,133,169,166,146,378,141,177,167,144,379,142,178,143,165,145,380,179,149,162,381,140,176,147,163,382,138,174,148,164,383,139,175,692,691,690,689,438,449,16,456,195,439,196,447,17,457,440,197,448,15,458,194,441,445,12,459,192,442,446,13,460,193,443,444,14,461,455,436,201,22,462,453,437,202,23,463,21,454,435,203,464,432,451,200,18,465,433,452,198,19,466,434,450,199,20,467,699,700,698,697,84,98,131,118,79,85,80,96,129,119,86,78,97,130,117,82,87,101,127,114,83,88,99,128,115,81,89,100,126,116,104,90,77,122,109,102,91,75,120,110,121,103,92,76,108,93,107,73,125,112,94,105,74,123,113,95,106,72,124,111,663,664,662,661,617,626,611,598,38,615,36,624,609,599,616,37,625,610,597,41,613,629,607,594,39,614,627,608,595,40,612,628,606,596,632,623,44,602,589,630,621,42,600,590,601,631,622,43,588,619,635,47,605,592,620,633,45,603,593,618,634,46,604,591,682,683,684,681,649,650,648,651,210,653,211,654,652,655,656,212,658,657,659,213,644,646,645,647,214,637,638,636,639,215,641,642,640,643,485,478,208,468,489,483,479,209,469,490,470,484,477,207,491,474,481,204,471,488,475,482,205,472,486,476,480,206,473,487,695,696,693,694,425,395,419,399,190,423,191,393,417,400,424,189,394,418,401,186,421,391,415,398,187,422,392,416,396,188,420,390,414,397,386,431,181,410,405,384,429,182,408,406,409,385,430,180,407,427,389,184,413,404,428,387,185,411,402,426,388,183,412,403,667,668,665,666,56,295,263,302,237,54,238,296,261,300,55,239,294,262,301,236,59,298,259,305,234,57,299,260,303,235,58,297,258,304,293,51,228,254,308,291,52,229,252,306,253,292,53,230,307,50,289,231,257,311,48,290,232,255,309,49,288,233,256,310,675,676,673,674 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#b25ea76719ef85ac96ca5a21eaa9f8d56a10b2e0f8b67970c90091297d765387, 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 19:51:40 · history