Equation 677 Database

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Magma 29da2a185230…

magma 29da2a185230
Size
705
Isomorphism class hash
29da2a18523008998f91d97be540b08d6d5975e682189a43a866fa86243920c6
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 15:59:51
Display reorder
660,610,2,387,406,403,407,1,608,388,404,405,0,609,389,402,5,613,390,409,399,391,611,3,410,400,612,4,392,408,401,8,385,616,412,394,6,386,614,413,395,7,384,615,411,393,11,381,619,415,397,9,382,617,416,398,383,10,618,414,396,687,688,686,685,294,202,204,485,221,483,203,295,205,219,484,201,296,206,220,198,297,207,488,217,208,298,199,486,218,299,200,209,487,216,193,210,292,480,227,194,211,293,481,225,192,212,291,482,226,196,213,288,479,223,197,214,289,477,224,215,195,290,478,222,703,704,701,702,599,61,365,58,371,59,62,600,363,369,57,60,601,364,370,64,598,368,54,374,366,596,65,55,372,597,63,367,56,373,67,360,605,49,377,68,361,606,50,375,66,362,607,48,376,70,359,604,52,380,71,357,602,53,378,358,69,603,51,379,671,672,670,669,228,512,146,495,23,496,510,229,144,24,497,511,230,145,22,508,231,149,498,19,147,232,509,499,20,233,507,148,500,21,503,152,234,493,14,501,150,235,494,15,502,151,236,492,13,506,155,237,489,17,504,153,238,490,18,154,505,239,491,16,679,680,678,677,524,278,240,274,255,275,276,522,241,256,273,277,523,242,257,281,520,243,270,254,244,521,279,271,252,519,280,245,272,253,284,246,515,265,261,282,247,513,266,262,283,248,514,264,263,287,249,518,268,260,285,250,516,269,258,251,286,517,267,259,692,691,690,689,179,327,32,317,579,315,328,177,33,580,316,329,178,31,581,326,175,35,313,582,36,176,324,314,583,174,325,34,312,584,333,30,170,323,577,334,28,168,321,578,335,29,169,322,576,332,26,173,319,573,330,27,171,320,574,25,331,172,318,575,699,700,698,697,131,101,111,84,81,85,99,129,112,82,86,100,130,113,83,97,127,110,87,80,108,128,98,88,78,126,96,109,89,79,107,117,122,90,72,105,118,120,91,73,106,119,121,92,74,103,116,125,93,75,104,114,123,94,76,115,102,124,95,77,663,664,662,661,418,642,646,626,189,627,643,419,644,190,628,641,417,645,191,638,421,649,629,188,647,422,639,630,186,420,640,648,631,187,633,652,424,624,180,634,650,425,625,181,632,651,423,623,182,636,655,427,620,183,637,653,428,621,184,654,635,426,622,185,682,683,684,681,140,349,343,593,46,591,350,138,344,47,592,348,139,342,45,12,143,346,595,37,656,141,657,658,659,142,347,345,594,44,355,341,135,588,40,356,339,136,589,38,354,340,137,590,39,351,337,134,587,43,352,338,132,585,41,336,353,133,586,42,695,696,693,694,156,565,531,550,546,551,566,157,532,547,549,564,158,533,548,561,159,534,553,545,535,160,562,554,543,161,563,536,552,544,571,529,162,556,537,572,530,163,557,538,570,528,164,555,539,567,525,165,559,540,568,526,166,560,541,527,569,167,558,542,667,668,665,666,300,444,462,434,467,432,445,301,463,465,433,446,302,464,466,443,303,461,430,470,459,304,441,431,468,305,442,460,429,469,450,453,306,440,473,451,454,307,438,471,452,455,308,439,472,449,456,309,436,476,447,457,310,437,474,458,448,311,435,475,675,676,673,674 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#2c9cca33fbeafeb683cb8962a04870775a8e5c306e9c00d15364712f8c215d93, 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 15:59:52 · history