Equation 677 Database

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Magma 61ae9c5fa560…

magma 61ae9c5fa560
Size
705
Isomorphism class hash
61ae9c5fa5609072f2428323cc8cf9cfa69646bb176aed6b1f0e1ac44ed72024
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 15:25:01
Display reorder
660,606,406,382,369,393,407,391,604,383,367,408,392,605,384,368,396,405,609,381,372,394,403,607,379,370,395,404,608,380,371,399,412,612,388,375,397,413,610,389,373,398,414,611,390,374,411,402,615,387,378,409,400,613,385,376,410,401,614,386,377,687,688,686,685,219,5,459,90,98,3,96,220,457,91,4,97,221,458,92,101,0,218,462,93,99,2,216,460,94,100,1,217,461,95,104,11,225,454,88,102,9,226,455,89,103,10,227,456,87,7,107,224,453,84,8,105,222,451,85,6,106,223,452,86,703,704,701,702,595,323,348,333,358,324,359,596,346,331,322,360,597,347,332,357,319,594,344,336,355,320,592,345,334,356,321,593,343,335,364,329,601,354,339,365,330,602,352,337,366,328,603,353,338,325,363,600,350,342,326,361,598,351,340,327,362,599,349,341,671,672,670,669,114,498,469,228,475,496,476,115,470,229,497,477,116,471,230,478,494,117,472,231,479,495,118,473,232,480,493,119,474,233,481,489,112,467,234,482,487,113,468,235,483,488,111,466,236,492,484,108,463,237,490,485,109,464,238,491,486,110,465,239,679,680,678,677,508,254,278,268,244,252,245,509,276,269,253,243,510,277,267,240,257,507,281,264,241,255,505,279,265,242,256,506,280,266,250,260,499,284,274,251,258,500,282,275,249,259,501,283,273,263,246,502,287,270,261,247,503,285,271,262,248,504,286,272,692,691,690,689,172,161,309,565,152,159,150,173,310,566,160,151,171,311,567,155,157,168,308,568,153,158,169,306,569,154,156,170,307,570,147,167,178,300,563,148,165,179,301,564,149,166,177,302,562,163,146,174,303,559,164,144,175,304,560,162,145,176,305,561,699,700,698,697,72,63,43,14,56,64,54,73,44,12,65,55,74,42,13,59,62,75,46,17,57,60,76,47,15,58,61,77,45,16,51,69,78,41,20,52,70,79,39,18,53,71,80,40,19,68,50,81,37,23,66,48,82,38,21,67,49,83,36,22,663,664,662,661,124,181,622,421,630,182,628,125,623,422,180,629,123,624,423,633,184,120,625,424,631,185,121,626,425,632,183,122,627,426,636,187,130,620,419,634,188,131,621,420,635,186,129,619,418,190,639,126,616,415,191,637,127,617,416,189,638,128,618,417,682,683,684,681,32,655,652,653,654,659,658,30,656,657,651,650,31,648,649,578,585,35,577,312,641,642,33,640,643,646,647,34,645,644,582,586,27,576,313,583,587,28,574,314,584,588,29,575,315,589,581,26,572,316,590,579,24,573,317,591,580,25,571,318,695,696,693,694,295,516,540,528,551,514,552,296,538,526,515,550,294,539,527,547,512,298,536,524,548,513,299,537,525,549,511,297,535,523,557,522,293,546,534,558,520,291,544,532,556,521,292,545,533,518,553,289,542,530,519,554,290,543,531,517,555,288,541,529,667,668,665,666,133,433,200,441,208,434,209,134,198,439,435,207,132,199,440,204,436,136,203,444,205,437,137,201,442,206,438,135,202,443,214,431,139,195,447,215,432,140,196,445,213,430,138,197,446,427,210,142,194,450,428,211,143,192,448,429,212,141,193,449,675,676,673,674 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#198f8683bee40b5fe0cfed42350fb71daef6a15506139cdcf5a71dcf11978025, 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 15:25:02 · history