Equation 677 Database

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Magma 770dc26c89d1…

magma 770dc26c89d1
Size
705
Isomorphism class hash
770dc26c89d1c73a7cf96cd61e96cad1d32c9cbb237e0714ef2c8d6723a72bb1
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 17:31:39
Display reorder
660,127,169,147,355,137,125,167,148,356,138,126,168,146,357,139,165,123,150,354,136,166,124,151,352,134,164,122,149,353,135,160,133,361,153,143,158,131,362,154,144,159,132,363,152,145,129,163,360,156,142,130,161,358,157,140,128,162,359,155,141,685,686,688,687,24,431,2,200,46,22,432,3,201,44,23,430,0,202,45,434,20,5,203,49,435,21,6,204,47,433,19,4,205,48,429,15,198,8,41,427,13,199,9,42,428,14,197,7,43,18,425,194,11,40,16,426,195,12,38,17,424,196,10,39,701,702,704,703,549,541,579,351,560,547,542,577,349,561,548,543,578,350,559,540,545,575,347,556,538,546,576,348,557,539,544,574,346,558,532,555,342,570,566,533,553,340,568,567,534,554,341,569,565,551,535,345,573,562,552,536,343,571,563,550,537,344,572,564,670,669,672,671,246,239,219,436,209,247,240,220,437,210,245,241,218,438,211,238,242,222,439,208,236,243,223,440,206,237,244,221,441,207,230,252,442,225,215,231,253,443,226,216,232,251,444,224,217,248,233,445,228,214,249,234,446,229,212,250,235,447,227,213,680,677,679,678,476,460,451,264,493,477,461,452,265,494,475,462,453,263,495,463,472,450,260,492,464,473,448,261,490,465,474,449,262,491,466,482,255,457,484,467,483,256,458,485,468,481,254,459,486,478,469,258,456,487,479,470,259,454,488,480,471,257,455,489,689,690,691,692,317,516,114,79,98,318,514,115,77,99,319,515,113,78,100,519,316,110,75,101,517,314,111,76,102,518,315,112,74,103,511,323,85,120,104,512,324,83,121,105,513,325,84,119,106,322,510,81,116,107,320,508,82,117,108,321,509,80,118,109,697,698,700,699,613,593,639,586,620,614,594,637,587,621,615,592,638,588,619,596,612,635,589,616,597,610,636,590,617,595,611,634,591,618,599,604,584,630,626,600,605,585,628,627,598,606,583,629,625,607,602,580,633,622,608,603,581,631,623,609,601,582,632,624,661,662,664,663,173,371,55,93,65,174,372,53,94,66,175,370,54,92,67,374,172,51,96,64,375,170,52,97,62,373,171,50,95,63,369,179,91,61,71,367,180,89,59,72,368,181,90,60,73,178,365,87,57,70,176,366,88,58,68,177,364,86,56,69,682,681,684,683,33,30,333,529,328,34,28,334,530,329,32,29,335,531,327,26,36,336,528,331,27,37,337,526,332,25,35,338,527,330,644,645,520,647,646,31,1,521,339,326,640,641,522,642,643,657,656,523,659,658,648,649,524,651,650,653,652,525,655,654,693,694,696,695,281,266,311,501,291,282,267,312,499,292,283,268,313,500,290,269,280,310,497,294,270,278,308,498,295,271,279,309,496,293,272,287,507,302,297,273,288,505,303,298,274,289,506,304,296,286,275,503,305,300,284,276,504,306,301,285,277,502,307,299,666,665,668,667,397,380,415,185,405,398,381,416,186,403,399,379,417,187,404,376,396,414,184,401,377,394,412,182,402,378,395,413,183,400,386,388,191,421,411,387,389,192,422,409,385,390,193,423,410,391,382,190,420,407,392,383,188,418,408,393,384,189,419,406,674,673,676,675 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#58758ff0293182d6dd53be73984d3e209a66569482d3b8502bf477ddaee58f10, 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 17:31:40 · history