Equation 677 Database

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Magma 5cb2fe8afd40…

magma 5cb2fe8afd40
Size
705
Isomorphism class hash
5cb2fe8afd4012a33807738f3a49d80d28a7a7e7a7229775736c86df10d36743
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 19:59:24
Display reorder
663,279,281,280,277,278,276,287,285,286,283,284,282,124,125,123,120,121,122,130,131,129,126,127,128,90,91,92,93,94,95,88,89,87,84,85,86,172,173,171,168,169,170,178,179,177,174,175,176,164,162,163,167,165,166,159,160,161,158,156,157,683,690,684,704,582,584,583,587,585,586,579,580,581,578,576,577,635,633,634,631,632,630,626,624,625,629,627,628,69,70,71,68,66,67,60,61,62,63,64,65,607,608,606,610,611,609,605,603,604,601,602,600,648,649,650,651,652,653,654,655,656,657,658,659,672,691,686,701,524,523,522,526,527,525,521,519,520,517,518,516,112,113,111,108,109,110,118,119,117,114,115,116,33,34,35,32,30,31,24,25,26,27,28,29,552,553,554,555,556,557,558,559,560,561,562,563,538,539,537,534,535,536,529,530,528,532,533,531,660,673,670,694,411,413,412,409,410,408,419,417,418,415,416,414,37,38,36,40,41,39,43,44,42,46,47,45,261,262,263,260,258,259,252,253,254,255,256,257,361,362,360,364,365,363,367,368,366,370,371,369,388,389,387,384,385,386,394,395,393,390,391,392,664,677,682,697,51,53,52,49,50,48,59,57,58,55,56,54,568,569,567,564,565,566,574,575,573,570,571,572,642,643,644,645,646,647,640,641,639,636,637,638,622,623,621,618,619,620,613,614,612,616,617,615,588,589,590,591,592,593,594,595,596,597,598,599,669,689,685,702,221,220,219,216,217,218,226,227,225,222,223,224,307,308,306,310,311,309,305,303,304,301,302,300,319,320,318,322,323,321,317,315,316,313,314,312,206,204,205,209,207,208,212,210,211,215,213,214,196,197,195,192,193,194,202,203,201,198,199,200,680,688,687,703,154,153,155,152,150,151,144,145,146,147,148,149,235,236,234,238,239,237,233,231,232,229,230,228,133,134,132,136,137,135,139,140,138,142,143,141,292,293,291,288,289,290,298,299,297,294,295,296,185,183,184,181,182,180,191,189,190,187,188,186,667,692,699,700,353,352,351,348,349,350,358,359,357,354,355,356,96,97,98,99,100,101,102,103,104,105,106,107,242,240,241,245,243,244,248,246,247,251,249,250,508,509,507,504,505,506,514,515,513,510,511,512,546,547,548,549,550,551,544,545,543,540,541,542,661,678,671,693,75,77,76,73,74,72,83,81,82,79,80,78,405,406,407,404,402,403,396,397,398,399,400,401,6,7,8,9,10,11,4,5,3,1,0,2,269,267,268,265,266,264,275,273,274,271,272,270,378,379,380,381,382,383,376,377,375,372,373,374,665,674,681,698,17,16,15,12,13,14,22,23,21,18,19,20,449,447,448,445,446,444,455,453,454,451,452,450,431,429,430,427,428,426,422,420,421,425,423,424,327,328,329,326,324,325,333,334,335,332,330,331,482,480,481,485,483,484,488,486,487,491,489,490,662,676,668,696,433,432,434,435,436,437,438,439,440,441,442,443,472,473,471,468,469,470,478,479,477,474,475,476,494,492,493,497,495,496,500,498,499,503,501,502,459,460,461,458,456,457,465,466,467,464,462,463,345,346,347,344,342,343,336,337,338,339,340,341,666,675,679,695 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {61} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 19:59:25 · history