Equation 677 Database

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Magma e66dcfbf0797…

magma e66dcfbf0797
Size
705
Isomorphism class hash
e66dcfbf0797f3305ab1b7b0d9193b0b9a8bccd293d0a2ed1272ca9f99a76f53
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 17:25:10
Display reorder
660,231,339,124,355,5,229,340,125,356,3,230,341,126,354,4,234,342,123,351,0,232,343,121,352,2,233,344,122,353,1,115,226,337,346,11,116,227,338,347,9,117,228,336,345,10,225,118,333,349,7,223,119,334,350,8,224,120,335,348,6,685,686,688,687,406,433,161,444,417,407,434,162,445,418,405,432,160,446,419,409,429,157,443,420,410,430,158,441,421,408,431,159,442,422,152,412,439,450,423,153,413,440,451,424,151,411,438,452,425,415,155,435,449,426,416,156,436,447,427,414,154,437,448,428,701,702,704,703,331,114,631,315,220,332,112,629,316,221,330,113,630,317,222,327,110,627,318,219,328,111,628,319,217,329,109,626,320,218,622,322,105,313,211,620,323,103,314,212,621,321,104,312,213,325,625,108,309,214,326,623,106,310,215,324,624,107,311,216,670,669,672,671,488,464,165,474,498,486,462,163,475,499,487,463,164,476,500,484,460,168,473,497,485,461,166,471,495,483,459,167,472,496,171,479,455,465,489,169,477,453,466,490,170,478,454,467,491,482,174,458,468,492,480,172,456,469,493,481,173,457,470,494,680,677,679,678,512,536,24,547,524,510,534,25,548,522,511,535,26,546,523,508,532,27,543,520,509,533,28,544,521,507,531,29,545,519,30,503,527,538,515,31,501,525,539,513,32,502,526,537,514,506,33,530,541,518,504,34,528,542,516,505,35,529,540,517,689,690,691,692,72,265,188,282,603,73,266,189,280,604,74,267,187,281,605,75,268,191,278,606,76,269,192,279,607,77,270,190,277,608,194,78,263,273,601,195,79,264,271,602,193,80,262,272,600,81,197,259,276,597,82,198,260,274,598,83,196,261,275,599,697,698,700,699,42,58,655,18,638,43,59,653,19,639,44,57,654,20,640,45,54,651,21,641,46,55,652,22,642,47,56,650,23,643,646,40,49,16,636,644,41,50,17,637,645,39,48,15,635,36,649,52,12,632,37,647,53,13,633,38,648,51,14,634,661,662,664,663,364,239,131,94,371,365,240,132,95,369,363,238,130,93,370,367,235,127,90,374,368,236,128,91,372,366,237,129,92,373,137,362,245,85,377,138,360,246,86,375,136,361,244,84,376,358,133,241,88,380,359,134,242,89,378,357,135,243,87,379,682,681,684,683,616,297,199,97,286,614,298,200,98,287,615,299,201,99,288,619,296,202,100,285,617,294,203,101,283,618,295,204,102,284,205,612,303,305,292,206,613,304,96,293,207,658,656,657,659,611,208,302,308,291,609,209,300,306,289,610,210,301,307,290,693,694,696,695,566,587,176,559,574,564,585,177,560,575,565,586,175,558,573,562,590,179,555,577,563,588,180,556,578,561,589,178,557,576,182,572,593,550,580,183,570,591,551,581,181,571,592,549,579,568,185,596,553,583,569,186,594,554,584,567,184,595,552,582,666,665,668,667,148,387,248,403,71,149,388,249,404,69,150,389,247,402,70,147,390,251,399,67,145,391,252,400,68,146,392,250,401,66,254,139,385,394,62,255,140,386,395,60,253,141,384,393,61,142,257,381,397,65,143,258,382,398,63,144,256,383,396,64,674,673,676,675 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#555d8536a50144822bfea9b20f3ef68710f5792b887e6dda4840627962426043, 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 17:25:11 · history