Equation 677 Database

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Magma 76ee166d1f94…

magma 76ee166d1f94
Size
705
Isomorphism class hash
76ee166d1f9486332b6e532cb1c3a3873aa3d2cd50f10cf703d4e89219c3ea68
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 15:22:46
Display reorder
660,442,479,184,466,454,443,185,467,455,477,441,478,183,465,453,475,438,180,462,450,476,439,181,463,451,474,440,182,464,452,190,448,485,472,460,449,483,473,191,461,447,484,471,189,459,481,444,468,186,456,482,445,469,187,457,480,446,470,188,458,685,686,688,687,279,267,530,255,244,280,528,256,245,268,281,269,529,257,243,266,278,533,254,240,264,276,531,252,241,265,277,532,253,242,525,285,273,261,250,286,274,262,526,251,287,275,263,527,249,272,284,260,524,246,270,282,258,522,247,271,283,259,523,248,701,702,704,703,168,162,436,627,612,169,437,625,610,163,170,164,435,626,611,165,171,432,623,615,166,172,433,624,613,167,173,434,622,614,427,174,160,618,607,175,161,616,428,608,176,159,617,426,609,156,177,621,430,606,157,178,619,431,604,158,179,620,429,605,670,669,672,671,293,556,66,542,102,291,67,540,103,557,292,555,68,541,104,552,289,69,545,105,553,290,70,543,106,554,288,71,544,107,64,299,547,537,100,297,548,538,65,101,298,546,539,63,99,550,295,536,60,96,551,296,534,61,97,549,294,535,62,98,680,677,679,678,304,566,76,113,316,305,77,111,317,564,303,565,75,112,315,569,300,72,109,312,567,301,73,110,313,568,302,74,108,314,82,310,561,119,322,311,562,117,83,323,309,563,118,81,321,560,306,115,78,318,558,307,116,79,319,559,308,114,80,320,689,690,691,692,352,388,587,375,364,353,585,376,365,389,351,387,586,377,363,384,348,583,374,360,385,349,584,372,361,386,350,582,373,362,593,358,394,381,370,359,395,382,591,371,357,393,383,592,369,390,354,380,589,366,391,355,378,590,367,392,356,379,588,368,697,698,700,699,636,43,651,26,23,634,649,24,21,44,635,42,650,25,22,46,639,647,29,19,47,637,648,27,20,45,638,646,28,18,642,631,41,32,14,632,39,30,640,12,633,40,31,641,13,37,630,35,645,17,38,628,33,643,15,36,629,34,644,16,661,662,664,663,120,135,198,500,492,121,199,498,493,136,122,137,200,499,494,134,123,201,503,495,132,124,202,501,496,133,125,203,502,497,196,126,141,506,490,127,142,504,197,491,128,143,505,195,489,140,129,509,192,486,138,130,507,193,487,139,131,508,194,488,682,681,684,683,399,424,148,600,407,400,149,598,405,425,401,423,147,599,406,420,402,144,603,410,421,403,145,601,408,422,404,146,602,409,154,657,658,659,656,415,416,597,155,411,652,653,654,153,655,418,396,596,150,414,419,397,594,151,412,417,398,595,152,413,693,694,696,695,330,6,573,92,336,331,574,90,337,7,332,8,575,91,338,9,333,572,95,339,10,334,570,93,340,11,335,571,94,341,579,328,4,87,342,329,5,88,580,343,327,3,89,581,344,1,324,86,578,345,0,325,84,576,346,2,326,85,577,347,666,665,668,667,204,516,54,233,219,205,55,231,220,517,206,518,56,232,221,519,207,57,229,218,520,208,58,230,216,521,209,59,228,217,52,210,514,239,225,211,515,237,53,226,212,513,238,51,227,510,213,235,48,224,511,214,236,49,222,512,215,234,50,223,674,673,676,675 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#164604ba66664ae7e7b126fe65d39300d84fb27e5ce614035873663e987c6567, 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 15:22:47 · history