Equation 677 Database

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Magma 116d7ae60880…

magma 116d7ae60880
Size
705
Isomorphism class hash
116d7ae60880fb03ce8303c7a683aa31a8acf7aea13491d0e085eef44ba84825
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 21:09:00
Display reorder
704,66,79,30,54,67,80,31,55,68,78,32,56,69,33,82,57,70,83,58,34,71,35,81,59,52,64,77,28,53,65,75,29,63,51,76,27,48,60,73,24,49,61,74,25,50,62,72,26,43,44,42,46,47,45,41,39,36,37,38,40,683,681,682,680,321,335,23,309,322,333,21,310,323,334,22,311,320,19,331,308,318,332,306,20,319,18,330,307,300,312,326,14,301,313,324,12,314,302,325,13,303,315,329,17,304,316,327,15,305,317,328,16,648,649,650,651,652,653,654,655,658,656,657,659,701,702,700,703,200,211,590,233,198,212,588,231,199,210,589,232,203,593,214,229,201,215,230,591,202,592,213,228,239,195,209,596,237,196,207,594,197,238,208,595,235,194,205,599,236,192,206,597,234,193,204,598,221,219,220,217,218,216,227,225,222,223,224,226,669,670,668,671,492,504,168,535,493,505,169,536,494,506,170,534,495,171,507,538,496,508,539,172,497,173,509,537,533,498,510,174,531,499,511,175,500,532,512,176,529,501,513,177,530,502,514,178,528,503,515,179,518,516,517,521,519,520,524,522,526,527,525,523,679,677,678,676,268,279,90,256,269,280,91,257,267,281,92,255,264,93,278,252,265,276,253,94,266,95,277,254,262,274,285,88,263,275,286,89,273,261,287,87,258,270,284,84,259,271,282,85,260,272,283,86,289,290,288,292,293,291,295,296,297,298,299,294,689,691,688,690,405,418,8,393,406,419,6,394,407,417,7,395,404,11,414,392,402,415,390,9,403,10,416,391,384,396,409,3,385,397,410,4,398,386,408,5,387,399,412,2,388,400,413,1,389,401,411,0,430,431,429,426,427,428,421,422,423,424,425,420,692,695,693,694,638,603,243,624,636,604,244,625,637,605,245,626,641,242,602,627,639,600,628,240,640,241,601,629,630,644,609,249,631,642,610,250,643,632,611,251,633,647,608,248,634,645,606,246,635,646,607,247,613,614,612,616,617,615,619,620,621,622,623,618,662,661,660,663,441,454,110,478,442,455,108,479,443,453,109,477,440,113,450,474,438,451,475,111,439,112,452,476,469,432,445,116,470,433,446,114,434,468,444,115,472,435,448,119,473,436,449,117,471,437,447,118,466,467,465,462,463,464,457,458,459,460,461,456,685,687,684,686,147,157,485,137,148,158,483,135,149,156,484,136,146,481,160,133,144,161,134,482,145,480,159,132,143,153,163,491,141,154,164,489,155,142,162,490,139,152,166,487,140,150,167,488,138,151,165,486,128,126,127,131,129,130,123,124,121,122,120,125,698,696,699,697,568,580,180,556,569,581,181,557,567,579,182,555,564,183,576,552,565,577,553,184,566,185,578,554,562,574,586,186,563,575,587,187,573,561,585,188,558,570,582,189,559,571,583,190,560,572,584,191,545,543,544,541,542,540,551,549,546,547,548,550,666,664,667,665,351,360,98,343,352,361,96,344,353,362,97,342,350,101,363,346,348,364,347,99,349,100,365,345,341,357,366,104,339,358,367,102,359,340,368,103,337,356,369,107,338,354,370,105,336,355,371,106,374,372,373,377,375,376,380,378,382,383,381,379,674,672,675,673 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#d999f02d519da9e6482c93589338b3231f65cc1ce6e36c19968e5d782b765397, 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 21:09:01 · history