Equation 677 Database

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Magma bb2b96589a69…

magma bb2b96589a69
Size
705
Isomorphism class hash
bb2b96589a69a19adc5274713f5b2666204b98f1381e1f0818fa3e8232d831ef
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 20:40:12
Display reorder
660,624,618,337,160,170,625,619,338,161,168,626,620,336,159,169,163,621,627,340,166,341,628,622,164,167,623,629,162,165,339,616,343,630,158,176,617,344,631,156,174,342,615,632,157,175,633,346,612,154,172,347,613,634,155,173,614,345,635,153,171,687,688,686,685,415,454,263,437,424,416,455,261,435,425,414,453,262,436,423,433,450,418,266,420,264,419,451,434,421,452,417,432,422,265,445,269,413,443,430,446,267,411,441,431,268,444,412,442,429,409,272,448,439,426,270,449,410,440,427,447,271,408,438,428,703,704,701,702,599,586,327,573,602,597,587,328,574,600,598,585,329,575,601,572,582,595,326,605,324,596,583,570,603,584,594,571,604,325,577,333,590,564,608,578,334,588,565,606,335,576,589,566,607,593,332,580,567,611,330,581,591,568,609,579,331,592,569,610,671,672,670,669,26,67,38,471,463,24,68,36,472,464,25,66,37,473,462,470,63,29,41,466,39,27,64,468,467,65,28,469,465,40,58,44,32,477,461,59,42,30,478,459,43,57,31,479,460,35,47,61,476,457,45,62,33,474,458,60,46,34,475,456,679,680,678,677,95,87,489,16,107,93,88,490,17,105,94,89,491,15,106,12,90,98,488,110,486,96,91,13,108,92,97,14,109,487,85,480,101,22,113,86,481,99,23,111,482,84,100,21,112,104,483,81,18,116,484,82,102,19,114,83,485,103,20,115,692,691,690,689,546,150,10,134,293,547,151,11,132,291,548,152,9,133,292,130,149,549,6,296,7,550,147,131,294,148,551,129,295,8,141,0,544,140,288,142,2,545,138,289,1,143,543,139,290,540,4,144,136,287,5,145,541,137,285,146,3,542,135,286,699,700,698,697,205,244,193,181,216,206,245,194,182,217,204,243,192,180,218,177,247,201,189,215,190,202,248,178,213,246,203,179,214,191,242,199,211,187,222,240,200,212,188,223,198,241,210,186,224,207,195,238,183,221,196,239,208,184,219,237,197,209,185,220,663,664,662,661,370,358,638,395,382,371,359,636,393,383,369,357,637,394,381,391,354,366,641,378,639,367,355,392,379,356,368,390,380,640,349,644,361,386,373,350,642,362,384,374,643,348,360,385,372,364,647,352,389,376,645,353,365,387,377,351,646,363,388,375,682,683,684,681,308,304,557,48,321,306,305,555,49,322,307,303,556,50,323,657,656,658,553,659,554,650,649,648,651,652,654,653,655,552,302,563,314,51,317,300,561,312,52,315,562,301,313,53,316,310,559,298,54,320,560,299,311,55,318,297,558,309,56,319,695,696,693,694,495,531,128,519,507,496,532,126,520,508,497,533,127,521,509,518,530,494,124,506,125,492,528,516,504,529,493,517,505,123,537,119,501,525,513,538,117,502,526,514,118,539,503,527,515,500,122,536,524,512,120,534,498,522,510,535,121,499,523,511,667,668,665,666,402,75,257,235,275,403,76,255,236,273,404,77,256,234,274,231,78,405,260,278,258,406,79,232,276,80,407,233,277,259,73,252,400,226,281,74,253,401,227,279,254,72,399,225,280,396,251,69,229,284,249,70,397,230,282,71,250,398,228,283,675,676,673,674 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#cb0e3d6c08ee89c5c6b2b247efbea2db23079510829d72f3f07184542ed1a6a6, 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 20:40:13 · history