Equation 677 Database

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Magma 32f8bc2393f3…

magma 32f8bc2393f3
Size
705
Isomorphism class hash
32f8bc2393f37112390977f3d73fcfa9b7f24b09af04c445715aa456d0a7cc6a
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 17:35:37
Display reorder
660,80,631,352,633,616,78,634,629,350,614,79,632,630,351,615,83,627,355,636,619,81,628,353,637,617,82,626,354,635,618,75,622,347,639,611,76,620,348,640,612,77,621,349,638,613,625,74,346,642,610,623,72,344,643,608,624,73,345,641,609,687,688,686,685,454,211,185,231,208,452,232,209,186,206,453,230,210,187,207,457,214,188,227,204,455,212,189,228,205,456,213,190,229,203,460,217,191,222,199,458,215,192,223,197,459,216,193,221,198,220,463,194,225,202,218,461,195,226,200,219,462,196,224,201,703,704,701,702,342,574,596,595,571,343,593,572,597,569,341,594,573,598,570,338,577,599,591,567,339,575,600,592,568,340,576,601,590,566,333,580,602,586,562,334,578,603,584,560,332,579,604,585,561,583,336,605,589,565,581,337,606,587,563,582,335,607,588,564,671,672,670,669,128,256,472,87,241,126,88,254,470,239,127,89,255,471,240,131,252,475,86,244,129,253,473,84,242,130,251,474,85,243,123,247,467,93,236,124,245,468,94,237,125,246,469,95,238,250,122,466,92,235,248,120,464,90,233,249,121,465,91,234,679,680,678,677,143,103,266,483,63,141,484,104,267,64,142,482,102,268,65,139,106,265,486,62,140,107,263,487,60,138,105,264,485,61,134,101,257,481,69,132,99,258,479,70,133,100,259,480,71,97,137,260,477,68,98,135,261,478,66,96,136,262,476,67,692,691,690,689,167,536,520,285,535,165,286,537,518,533,166,284,538,519,534,163,539,523,281,531,164,540,521,282,532,162,541,522,283,530,158,542,515,291,526,156,543,516,292,524,157,544,517,290,525,545,161,514,287,529,546,159,512,288,527,547,160,513,289,528,699,700,698,697,1,27,57,38,22,0,36,28,58,23,2,37,29,59,21,3,26,56,41,18,4,24,54,39,19,5,25,55,40,20,6,33,48,44,13,7,34,49,42,14,8,35,50,43,12,32,9,51,47,16,30,10,52,45,17,31,11,53,46,15,663,664,662,661,646,379,402,382,358,644,380,377,403,356,645,381,378,401,357,649,375,398,385,361,647,376,399,383,359,648,374,400,384,360,652,370,393,388,364,650,368,394,386,362,651,369,392,387,363,373,655,396,391,367,371,653,397,389,365,372,654,395,390,366,682,683,684,681,553,323,171,300,313,551,301,324,172,314,552,299,325,170,312,549,322,168,303,310,550,658,657,656,659,548,321,169,302,311,559,329,305,298,316,557,330,306,296,317,558,331,304,297,315,328,555,308,294,319,326,556,309,295,320,327,554,307,293,318,695,696,693,694,274,503,116,150,494,272,151,504,114,495,273,152,505,115,496,270,502,119,153,497,271,500,117,154,498,269,501,118,155,499,280,509,111,148,492,278,510,112,149,493,279,511,113,147,491,508,276,110,144,488,506,277,108,145,489,507,275,109,146,490,667,668,665,666,182,419,445,429,405,183,430,420,443,406,184,428,421,444,404,181,418,441,432,408,179,416,442,433,409,180,417,440,431,407,173,425,451,435,411,174,426,449,436,412,175,427,450,434,410,424,176,447,438,414,422,177,448,439,415,423,178,446,437,413,675,676,673,674 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#5a6f57af4478d367dfac6487e89f811f842218c665866e576bd9224bcbc8a047, 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 17:35:38 · history