Equation 677 Database

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Magma 0dbe23bf87f1…

magma 0dbe23bf87f1
Size
705
Isomorphism class hash
0dbe23bf87f1b2edb55f2d2f1af9e745750626cf791aae97423b08e87e7e6461
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 19:56:39
Display reorder
660,9,392,396,606,600,397,10,604,598,390,398,11,391,605,599,395,8,388,609,603,389,6,393,607,601,394,7,387,608,602,383,402,612,1,595,381,403,610,0,596,382,404,611,2,597,401,386,615,3,594,399,384,613,4,592,5,400,385,614,593,687,688,686,685,203,436,28,128,123,29,204,129,121,437,27,202,435,127,122,24,199,439,131,126,440,200,25,132,124,26,201,438,130,125,434,34,134,209,118,432,35,135,210,119,433,33,133,208,120,30,430,137,205,117,31,431,138,206,115,207,32,429,136,116,703,704,701,702,380,580,282,576,56,280,378,574,57,581,281,379,582,575,55,278,376,583,579,59,584,377,279,577,60,277,375,585,578,58,586,273,571,371,62,587,271,572,369,63,588,272,573,370,61,276,589,570,374,65,274,590,568,372,66,373,275,591,569,64,671,672,670,669,219,464,470,450,477,468,217,451,478,462,469,218,463,452,479,466,222,460,449,480,461,220,467,447,481,465,221,459,448,482,455,476,441,214,483,453,474,442,215,484,454,475,443,216,485,472,458,444,213,486,473,456,445,211,487,212,471,457,446,488,679,680,678,677,491,252,301,235,231,302,489,236,229,250,303,490,251,237,230,304,494,248,238,234,249,492,305,239,232,306,493,247,240,233,258,299,241,497,226,256,300,242,495,227,257,298,243,496,228,295,254,244,500,225,296,255,245,498,223,499,297,253,246,224,692,691,690,689,331,522,534,552,548,535,332,553,546,523,536,333,524,554,547,533,334,521,551,544,519,335,531,549,545,532,336,520,550,543,513,525,558,337,539,514,526,559,338,537,515,527,560,339,538,528,516,557,340,542,529,517,555,341,540,342,530,518,556,541,699,700,698,697,78,289,84,113,92,82,76,114,93,290,83,77,291,112,91,80,74,292,109,95,293,75,81,110,96,79,73,294,111,94,287,90,104,69,98,288,88,105,67,99,286,89,103,68,97,86,283,107,72,101,87,284,108,70,102,71,85,285,106,100,663,664,662,661,353,630,148,624,411,149,354,622,412,628,150,352,629,623,413,147,349,633,627,414,631,350,145,625,415,146,351,632,626,416,636,139,619,344,409,634,140,620,345,410,635,141,621,343,408,142,639,618,347,405,143,637,616,348,406,346,144,638,617,407,682,683,684,681,45,652,655,653,654,659,43,656,658,657,651,44,648,649,650,567,48,36,362,361,641,46,642,640,643,647,47,646,645,644,363,566,42,51,356,364,564,40,49,357,365,565,41,50,355,562,366,38,54,359,563,367,39,52,360,53,561,368,37,358,695,696,693,694,259,508,312,13,321,310,260,14,319,509,311,261,507,12,320,308,262,511,16,324,512,263,309,17,322,307,264,510,15,323,506,318,19,265,327,504,316,20,266,325,505,317,18,267,326,314,502,22,268,330,315,503,23,269,328,270,313,501,21,329,667,668,665,666,423,156,165,187,177,163,424,188,175,154,164,425,155,189,176,168,426,152,190,180,153,427,166,191,178,167,428,151,192,179,162,171,193,421,183,160,169,194,422,181,161,170,195,420,182,174,158,196,417,186,172,159,197,418,184,419,173,157,198,185,675,676,673,674 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#b7ef46c52e3181531ee451cc516c519f12d29148a838b2a4381cb7ae279fb33d, 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 19:56:40 · history