Equation 677 Database

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Magma 4011b2f500aa…

magma 4011b2f500aa
Size
705
Isomorphism class hash
4011b2f500aaa8d80ee6321af14920a5c7270d8e1c5d4c8802385e8930a6f55e
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 17:37:40
Display reorder
660,70,375,397,402,370,371,376,71,398,403,377,369,69,396,404,373,66,378,393,401,67,374,379,394,399,372,68,380,395,400,388,368,61,381,408,366,62,382,389,409,367,60,383,387,410,64,364,384,391,407,65,365,385,392,405,63,363,386,390,406,685,686,688,687,485,121,85,107,150,151,122,483,86,105,120,152,484,84,106,153,488,124,88,103,486,154,125,89,104,155,487,123,87,102,91,148,491,127,98,149,489,128,92,96,147,490,126,90,97,494,144,130,94,101,492,145,131,95,99,493,146,129,93,100,701,702,704,703,195,606,623,340,362,360,607,196,621,341,608,361,197,622,339,358,194,609,619,343,192,359,610,620,344,357,193,611,618,342,614,353,201,604,346,351,202,605,612,347,352,203,603,613,345,200,356,600,617,349,198,354,601,615,350,199,355,602,616,348,670,669,672,671,164,111,503,509,143,141,112,162,501,507,113,142,163,502,508,139,167,110,506,512,165,140,108,504,510,138,166,109,505,511,498,134,159,117,515,132,160,118,499,513,133,161,119,500,514,158,137,116,497,518,156,135,114,495,516,157,136,115,496,517,680,677,679,678,247,533,547,174,526,527,531,248,548,175,532,525,246,546,176,529,250,536,543,177,251,530,534,544,178,528,249,535,545,179,553,524,245,539,172,522,243,537,554,173,523,244,538,552,171,241,520,542,549,168,242,521,540,550,169,240,519,541,551,170,689,690,691,692,583,298,305,273,277,278,299,584,303,274,297,276,582,304,275,280,579,294,301,272,580,281,295,302,270,279,581,296,300,271,311,283,589,289,264,284,590,290,309,265,282,588,288,310,266,585,286,292,307,267,586,287,293,308,268,587,285,291,306,269,697,698,700,699,205,630,647,225,229,230,631,206,645,226,632,228,204,646,227,232,208,633,643,224,209,233,634,644,222,231,207,635,642,223,638,235,211,628,216,236,212,629,636,217,234,210,627,637,218,214,238,624,641,219,215,239,625,639,220,213,237,626,640,221,661,662,664,663,77,418,423,26,40,41,419,75,424,24,417,39,76,425,25,36,73,421,426,29,74,37,422,427,27,38,72,420,428,28,429,46,83,416,32,47,81,414,430,30,45,82,415,431,31,79,42,412,432,35,80,43,413,433,33,78,44,411,434,34,682,681,684,683,10,319,324,333,595,596,320,11,325,334,318,594,9,326,335,598,6,315,323,332,7,599,316,321,330,597,8,317,322,331,654,655,0,653,652,659,2,657,658,656,650,1,648,649,651,4,592,313,329,338,5,593,314,327,336,3,591,312,328,337,693,694,696,695,18,563,567,189,259,260,561,19,568,190,562,258,20,569,191,262,21,566,570,188,22,263,564,571,186,261,23,565,572,187,573,257,16,558,180,255,17,559,574,181,256,15,560,575,182,12,253,557,576,183,13,254,555,577,184,14,252,556,578,185,666,665,668,667,58,460,481,436,456,457,461,59,482,437,459,458,57,480,435,455,54,463,477,439,55,453,464,478,440,454,56,462,479,438,472,447,49,466,442,448,50,467,473,443,449,48,465,471,441,52,450,469,475,445,53,451,470,476,446,51,452,468,474,444,674,673,676,675 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#5b838974e03a318bd69da9937fbfbee1bd56d732e0aad8a944a467873e322378, 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 17:37:41 · history