Equation 677 Database

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Magma 269b64f79f6b…

magma 269b64f79f6b
Size
705
Isomorphism class hash
269b64f79f6b17153386537e322e4219531f34637cf6192e93d12d63239fd350
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 15:18:57
Display reorder
704,18,53,43,24,44,51,25,19,20,52,42,26,21,49,46,27,22,50,47,28,23,48,45,29,41,30,59,16,39,31,57,17,40,32,58,15,33,37,55,12,34,38,56,13,35,36,54,14,62,63,61,71,70,60,65,66,67,68,69,64,681,683,682,680,4,286,273,549,274,287,550,5,3,285,275,551,1,282,272,548,0,283,270,546,2,284,271,547,264,540,277,10,265,541,278,11,266,542,276,9,543,267,280,6,544,268,281,7,545,269,279,8,648,649,650,651,652,653,654,655,658,656,657,659,702,701,700,703,99,427,419,405,417,428,406,100,101,426,418,407,98,430,415,404,96,431,416,402,97,429,414,403,410,396,425,105,408,397,423,106,409,398,424,107,399,413,421,104,400,411,422,102,401,412,420,103,432,433,434,435,436,437,438,439,443,441,442,440,670,669,668,671,383,220,263,249,261,221,250,381,382,219,262,251,379,216,259,248,380,217,260,246,378,218,258,247,254,240,226,374,252,241,227,372,253,242,225,373,243,257,222,377,244,255,223,375,245,256,224,376,236,234,235,239,237,238,231,232,229,230,228,233,677,679,678,676,92,517,510,500,511,518,498,90,91,516,512,499,95,520,513,503,93,521,514,501,94,519,515,502,508,495,523,87,509,496,524,88,507,497,522,89,494,504,526,86,492,505,527,84,493,506,525,85,531,532,533,530,528,529,537,538,535,536,534,539,691,689,688,690,304,645,633,621,634,646,622,305,303,647,635,623,300,644,632,620,301,642,630,618,302,643,631,619,624,612,636,310,625,613,637,311,626,614,638,309,615,627,639,306,616,628,640,307,617,629,641,308,608,606,607,611,609,610,603,604,601,602,600,605,695,692,693,694,118,490,472,459,473,491,460,119,117,489,471,461,114,486,468,458,115,487,469,456,116,488,470,457,478,465,481,109,479,466,482,110,477,467,480,108,464,474,484,112,462,475,485,113,463,476,483,111,446,444,445,449,447,448,452,450,454,455,453,451,661,662,660,663,81,323,355,344,356,321,342,82,83,322,354,343,80,319,358,347,78,320,359,345,79,318,357,346,353,339,314,72,351,340,312,73,352,341,313,74,338,349,317,75,336,350,315,76,337,348,316,77,335,333,334,331,332,330,326,324,328,329,327,325,687,685,684,686,369,191,178,209,179,189,207,370,371,190,177,208,368,187,174,205,366,188,175,206,367,186,176,204,169,215,182,360,170,213,180,361,168,214,181,362,211,172,185,363,212,173,183,364,210,171,184,365,202,203,201,198,199,200,193,194,195,196,197,192,696,698,699,697,385,142,130,164,131,143,162,386,384,141,129,163,388,138,126,167,389,139,127,165,387,140,128,166,121,159,133,391,122,160,134,392,120,161,132,390,158,124,136,394,156,125,137,395,157,123,135,393,151,152,150,154,155,153,149,147,144,145,146,148,664,666,667,665,292,580,571,560,572,581,558,293,291,579,570,559,288,576,574,563,289,577,575,561,290,578,573,562,569,555,586,298,567,556,587,299,568,557,585,297,554,565,582,294,552,566,583,295,553,564,584,296,596,594,595,599,597,598,591,592,589,590,588,593,672,674,675,673 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#14697465b8cd7575930ebcd6f1cfb0d098649f4474b7abfd50cfc1485faac906, 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 15:18:58 · history