Equation 677 Database

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Magma cf5d31330580…

magma cf5d31330580
Size
705
Isomorphism class hash
cf5d3133058084c4861b52e96163c57e6f1e31a1842a6f8280d9b02e6fd8572f
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 16:57:20
Display reorder
660,89,304,312,327,288,289,305,87,313,328,290,303,88,314,329,291,85,300,315,326,86,292,301,316,324,293,84,302,317,325,95,310,294,318,333,93,311,295,319,334,320,94,309,296,335,306,91,297,321,332,307,92,298,322,330,308,90,299,323,331,685,686,688,687,195,434,404,417,424,425,432,196,402,418,423,433,197,403,419,420,194,437,407,416,192,421,435,405,414,422,193,436,406,415,201,440,430,399,408,202,438,431,400,409,401,203,439,429,410,443,200,426,398,411,441,198,427,396,412,442,199,428,397,413,701,702,704,703,72,278,588,602,604,605,276,73,586,603,606,277,74,587,601,607,75,281,591,598,76,608,279,589,599,609,77,280,590,600,78,284,610,583,593,79,282,611,584,594,585,80,283,612,592,287,81,613,582,596,285,82,614,580,597,286,83,615,581,595,670,669,672,671,103,209,450,466,469,470,207,104,451,467,468,208,102,452,465,472,106,205,453,462,107,473,206,454,463,471,105,204,455,464,101,215,475,448,457,99,213,476,449,458,447,100,214,474,456,211,97,478,444,460,212,98,479,445,461,210,96,477,446,459,680,677,679,678,114,239,488,502,221,219,237,115,486,503,220,238,116,487,501,217,117,235,491,498,118,218,236,489,499,216,119,234,490,500,112,230,227,483,493,113,228,225,484,494,485,111,229,226,492,233,108,223,482,496,231,109,224,480,497,232,110,222,481,495,689,690,691,692,261,516,533,549,556,557,517,262,531,550,555,518,263,532,551,552,260,519,529,548,258,553,520,530,546,554,259,521,528,547,252,522,562,539,540,253,523,563,537,541,538,254,524,561,542,525,255,558,535,543,526,256,559,536,544,527,257,560,534,545,697,698,700,699,32,622,639,47,51,52,623,30,637,45,53,624,31,638,46,50,35,625,635,43,33,48,626,636,44,49,34,627,634,42,27,620,57,630,38,28,621,58,628,36,629,29,619,59,37,616,26,56,633,41,617,24,54,631,39,618,25,55,632,40,661,662,664,663,179,359,364,374,342,343,357,177,365,372,344,358,178,363,373,345,175,355,360,377,176,346,356,361,375,347,174,354,362,376,170,350,340,370,380,168,348,341,371,378,369,169,349,339,379,353,173,336,366,383,351,171,337,367,381,352,172,338,368,382,682,681,684,683,274,159,575,566,166,167,160,275,573,564,165,161,273,574,565,162,270,158,578,569,271,163,156,576,567,164,272,157,577,568,265,646,645,647,644,266,572,571,579,570,642,264,641,640,643,657,268,656,659,658,648,269,649,651,650,653,267,652,655,654,693,694,696,695,504,143,147,247,125,123,141,505,148,248,124,142,506,149,246,121,507,139,146,250,508,122,140,144,251,120,509,138,145,249,510,134,131,153,245,511,132,129,154,243,155,512,133,130,244,137,513,127,152,241,135,514,128,150,242,136,515,126,151,240,666,665,668,667,66,17,188,1,390,391,15,67,186,0,392,16,68,187,2,393,69,13,191,3,70,394,14,189,4,395,71,12,190,5,64,23,388,183,6,65,21,389,184,7,185,63,22,387,8,19,60,384,182,9,20,61,385,180,10,18,62,386,181,11,674,673,676,675 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#4af6d9f6d3730a7119657046629cd5cdd39170988afb99e43673591a2135edbf, 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 16:57:22 · history