Equation 677 Database

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Magma ae52a703eedd…

magma ae52a703eedd
Size
705
Isomorphism class hash
ae52a703eedda42c92e45eb047a169081faec69fec7ddcbf6316606b053480e7
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 19:55:12
Display reorder
660,35,510,515,500,504,33,530,535,520,524,34,490,495,480,484,430,31,435,423,424,451,32,453,449,450,470,30,475,463,464,26,630,635,622,624,24,650,655,642,644,25,610,615,602,604,550,29,555,542,544,570,27,575,562,564,590,28,595,582,584,694,699,690,696,291,508,509,512,507,292,528,529,532,527,293,488,489,492,487,428,290,429,432,427,456,288,457,458,445,468,289,469,472,467,297,628,629,632,627,298,648,649,652,647,299,608,609,612,607,548,296,549,552,547,568,294,569,572,567,588,295,589,592,587,691,695,687,689,134,340,198,328,304,132,341,199,329,305,133,339,200,327,303,336,137,201,324,300,337,135,202,325,301,338,136,203,326,302,140,346,196,334,310,138,347,197,335,311,139,345,195,333,309,342,143,192,330,306,343,141,193,331,307,344,142,194,332,308,667,663,668,674,166,376,400,65,1,167,377,401,63,0,165,375,399,64,2,372,162,396,61,3,373,163,397,62,4,374,164,398,60,5,157,382,406,71,6,158,383,407,69,7,156,381,405,70,8,378,160,402,67,9,379,161,403,68,10,380,159,404,66,11,664,677,672,680,259,516,506,501,514,260,536,526,521,534,258,496,486,481,494,436,262,426,420,434,447,263,444,443,446,476,261,466,461,474,257,636,626,620,634,255,656,646,641,654,256,616,606,600,614,556,253,546,540,554,576,254,566,560,574,596,252,586,581,594,700,703,698,702,18,517,518,519,511,19,537,538,539,531,20,497,498,499,491,437,21,438,439,431,440,22,441,442,452,478,23,477,479,471,16,638,637,639,631,17,657,658,659,651,15,618,617,619,611,557,12,558,559,551,577,13,578,579,571,598,14,597,599,591,701,692,685,697,39,502,513,505,503,40,522,533,525,523,41,482,493,485,483,421,38,433,425,422,454,36,459,455,448,460,37,473,465,462,45,621,633,625,623,46,640,653,645,643,47,601,613,605,603,541,44,553,545,543,561,42,573,565,563,580,43,593,585,583,688,704,686,693,53,225,228,243,206,51,226,229,244,204,52,227,230,245,205,224,49,231,242,209,222,50,232,240,207,223,48,233,241,208,59,216,234,249,212,57,217,235,250,210,58,218,236,251,211,219,55,237,248,215,220,56,238,246,213,221,54,239,247,214,665,662,679,669,152,182,364,412,178,150,180,365,413,179,151,181,363,411,177,185,155,360,408,174,183,153,361,409,175,184,154,362,410,176,147,188,370,418,169,148,186,371,419,170,149,187,369,417,168,191,146,366,414,172,189,144,367,415,173,190,145,368,416,171,681,673,684,671,282,388,117,121,73,283,389,118,122,74,284,387,119,120,72,384,285,116,124,76,385,286,114,125,77,386,287,115,123,75,280,394,108,127,79,281,395,109,128,80,279,393,110,126,78,390,276,111,130,82,391,277,112,131,83,392,278,113,129,81,683,678,675,676,87,268,316,104,352,88,269,317,102,353,89,267,315,103,351,264,86,312,107,348,265,84,313,105,349,266,85,314,106,350,93,274,322,99,358,94,275,323,100,359,95,273,321,101,357,270,92,318,98,354,271,90,319,96,355,272,91,320,97,356,682,670,661,666 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#b3dac6ff36f26cacc8049b7c1e09fd794a0277a3d237510b4c6377f158398334, M = {60} 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 19:55:13 · history