Equation 677 Database

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Magma acbe2eb2b772…

magma acbe2eb2b772
Size
705
Isomorphism class hash
acbe2eb2b772a67d1a4ad209c9a0dcdefefb3aa430b1ce02bd6b7e65732bc22a
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 20:38:40
Display reorder
660,272,577,307,292,299,578,293,270,308,297,576,291,271,306,298,580,288,275,310,295,581,289,273,311,296,579,290,274,309,294,313,278,283,583,305,314,276,284,584,303,312,277,282,582,304,281,316,286,586,301,279,317,287,587,302,280,315,285,585,300,687,688,686,685,414,34,407,380,400,35,378,415,405,401,33,379,416,406,399,30,383,417,403,396,31,381,418,404,397,32,382,419,402,398,413,420,386,25,391,411,421,384,26,392,412,422,385,24,390,423,409,389,28,394,424,410,387,29,395,425,408,388,27,393,703,704,701,702,60,265,10,571,16,266,572,61,11,17,264,570,62,9,15,268,574,63,6,12,269,575,64,7,13,267,573,65,8,14,0,58,569,263,22,2,59,567,261,23,1,57,568,262,21,54,4,565,259,18,55,5,566,260,19,56,3,564,258,20,671,672,670,669,439,160,431,453,462,161,454,440,429,463,159,455,438,430,464,156,452,442,427,465,157,450,443,428,466,158,451,441,426,467,437,445,459,151,468,435,446,460,152,469,436,444,461,150,470,448,433,458,154,471,449,434,456,155,472,447,432,457,153,473,679,680,678,677,474,173,510,496,503,171,497,475,511,501,172,495,476,512,502,169,492,477,513,499,170,493,478,514,500,168,494,479,515,498,516,480,487,164,509,517,481,488,162,507,518,482,486,163,508,483,519,490,167,505,484,520,491,165,506,485,521,489,166,504,692,691,690,689,212,545,203,233,236,543,231,210,201,234,544,232,211,202,235,541,229,215,199,239,542,230,213,200,237,540,228,214,198,238,209,218,224,536,242,207,216,222,534,240,208,217,223,535,241,221,205,227,539,245,219,206,225,537,243,220,204,226,538,244,699,700,698,697,101,69,78,103,117,70,104,99,79,118,71,102,100,80,119,68,106,97,81,116,66,107,98,82,114,67,105,96,83,115,84,92,109,75,123,85,90,110,76,124,86,91,108,77,125,95,87,112,74,122,93,88,113,72,120,94,89,111,73,121,663,664,662,661,588,318,626,610,617,319,611,589,624,615,320,609,590,625,616,321,606,591,629,613,322,607,592,627,614,323,608,593,628,612,632,594,601,324,623,630,595,602,325,621,631,596,600,326,622,597,635,604,327,619,598,633,605,328,620,599,634,603,329,618,682,683,684,681,648,247,651,649,650,248,653,652,655,654,246,656,657,659,658,250,644,645,647,646,251,637,636,638,639,249,641,640,643,642,559,39,547,253,557,560,40,548,254,555,558,41,546,252,556,38,562,550,256,553,36,563,551,257,554,37,561,549,255,552,695,696,693,694,129,524,191,138,181,522,139,130,189,182,523,140,131,190,180,527,141,128,187,184,525,142,126,188,185,526,143,127,186,183,197,135,144,530,179,195,136,145,528,177,196,137,146,529,178,134,193,147,533,175,132,194,148,531,176,133,192,149,532,174,667,668,665,666,354,44,353,375,332,42,376,355,351,330,43,377,356,352,331,47,374,357,349,335,45,372,358,350,333,46,373,359,348,334,344,360,366,50,338,342,361,367,48,336,343,362,368,49,337,363,347,369,53,341,364,345,370,51,339,365,346,371,52,340,675,676,673,674 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#c8b00e8ba82c54826bf93ef2b9b2d8eeb61b8eb7ac0797b661231f1bb38e050b, 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 20:38:41 · history