Equation 677 Database

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Magma a558968ee36e…

magma a558968ee36e
Size
705
Isomorphism class hash
a558968ee36ee3d731e2c0776a079f25def18495477f7b196f3305573dd81382
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 21:47:20
Display reorder
660,147,149,148,145,146,144,155,153,154,151,152,150,162,163,164,165,166,167,160,161,159,156,157,158,376,377,375,372,373,374,382,383,381,378,379,380,141,142,143,140,138,139,132,133,134,135,136,137,43,44,42,46,47,45,41,39,40,37,38,36,681,685,688,683,457,456,458,459,460,461,462,463,464,465,466,467,469,470,468,472,473,471,475,476,474,478,479,477,489,490,491,488,486,487,480,481,482,483,484,485,455,453,454,451,452,450,446,444,445,449,447,448,50,48,49,53,51,52,56,54,55,59,57,58,693,692,703,697,365,364,363,360,361,362,370,371,369,366,367,368,325,326,324,328,329,327,331,332,330,334,335,333,345,346,347,344,342,343,336,337,338,339,340,341,357,358,359,356,354,355,348,349,350,351,352,353,27,28,29,26,24,25,33,34,35,32,30,31,665,670,675,672,520,519,521,518,516,517,525,526,527,524,522,523,535,536,534,538,539,537,533,531,532,529,530,528,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,67,68,66,70,71,69,65,63,64,61,62,60,678,682,686,684,549,551,550,547,548,546,542,540,541,545,543,544,563,561,562,559,560,558,554,552,553,557,555,556,106,107,105,102,103,104,97,98,96,100,101,99,119,117,118,115,116,114,110,108,109,113,111,112,195,196,197,194,192,193,201,202,203,200,198,199,691,696,702,700,648,650,649,653,651,652,656,654,655,659,657,658,613,614,612,616,617,615,619,620,618,622,623,621,635,633,634,631,632,630,626,624,625,629,627,628,647,645,646,643,644,642,638,636,637,641,639,640,271,272,270,274,275,273,269,267,268,265,266,264,689,695,704,699,247,246,248,249,250,251,244,245,243,240,241,242,209,207,208,205,206,204,215,213,214,211,212,210,222,223,224,225,226,227,220,221,219,216,217,218,236,234,235,239,237,238,231,232,233,230,228,229,253,254,252,256,257,255,259,260,258,262,263,261,662,661,663,664,425,424,423,420,421,422,430,431,429,426,427,428,385,386,384,388,389,387,391,392,390,394,395,393,405,406,407,404,402,403,396,397,398,399,400,401,417,418,419,416,414,415,408,409,410,411,412,413,170,168,169,173,171,172,176,174,175,179,177,178,677,680,687,679,301,300,302,303,304,305,306,307,308,309,310,311,313,314,312,316,317,315,319,320,318,322,323,321,286,287,285,282,283,284,277,278,276,280,281,279,299,297,298,295,296,294,290,288,289,293,291,292,4,5,3,1,0,2,10,11,9,6,7,8,690,694,701,698,591,593,592,589,590,588,599,597,598,595,596,594,608,606,607,611,609,610,603,604,605,602,600,601,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,128,126,127,131,129,130,123,124,125,122,120,121,666,671,674,673,94,93,95,92,90,91,84,85,86,87,88,89,441,442,443,440,438,439,432,433,434,435,436,437,182,180,181,185,183,184,188,186,187,191,189,190,78,79,80,81,82,83,76,77,75,72,73,74,21,22,23,20,18,19,12,13,14,15,16,17,668,669,676,667 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, 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 21:47:20 · history