Equation 677 Database

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Magma 2c312a28e721…

magma 2c312a28e721
Size
705
Isomorphism class hash
2c312a28e7210c5714d16cf96c074662f714d02e0a8e11b25aa36c93c9e536cb
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 19:18:49
Display reorder
660,509,507,508,41,511,39,529,527,528,531,487,40,489,488,491,37,429,428,420,431,38,450,448,449,451,36,469,467,468,471,629,627,628,47,631,649,647,648,45,651,609,607,608,46,611,549,547,548,43,553,569,567,568,44,573,589,587,588,42,593,701,689,687,690,516,503,504,260,506,258,536,523,524,526,483,259,496,484,486,263,436,424,425,427,261,459,456,457,445,262,476,463,464,466,636,623,624,255,626,656,643,644,256,646,616,603,604,257,606,558,543,544,254,546,578,563,564,252,566,598,583,584,253,586,699,696,702,685,280,304,340,141,388,142,281,305,341,389,303,143,279,339,387,140,276,300,336,384,138,277,301,337,385,139,278,302,338,386,286,310,346,132,394,287,311,347,133,395,285,309,345,134,393,282,306,342,135,390,283,307,343,136,391,284,308,344,137,392,665,680,664,673,205,228,219,62,195,60,206,229,220,196,230,61,204,221,197,65,208,231,218,194,63,209,232,216,192,64,207,233,217,193,211,234,225,68,201,212,235,226,66,202,210,236,227,67,203,214,237,224,71,200,215,238,222,69,198,213,239,223,70,199,663,677,669,666,515,505,510,189,500,190,535,525,530,520,485,191,495,490,480,188,435,426,430,422,186,447,444,446,443,187,475,465,470,460,635,625,630,180,621,655,645,650,181,640,615,605,610,182,601,557,545,550,183,540,577,565,570,184,560,597,585,590,185,580,688,697,700,694,519,518,517,19,514,20,539,538,537,534,498,18,499,497,494,22,439,438,437,434,23,442,441,440,453,21,479,477,478,474,639,637,638,17,634,657,659,658,15,654,619,617,618,16,614,559,552,551,13,556,579,572,571,14,576,599,592,591,12,596,695,691,704,693,512,502,501,6,513,7,532,522,521,533,482,8,492,481,493,9,432,423,421,433,10,458,455,454,452,11,472,462,461,473,632,622,620,4,633,652,642,641,5,653,612,602,600,3,613,554,542,541,1,555,574,562,561,0,575,594,582,581,2,595,703,686,698,692,268,153,174,251,405,249,269,154,175,407,155,250,267,176,403,247,264,152,177,397,248,265,150,178,399,246,266,151,179,401,274,144,172,242,416,275,145,173,240,418,273,146,171,241,414,270,147,168,245,408,271,148,169,243,410,272,149,170,244,412,683,682,661,675,364,114,51,82,131,83,365,115,52,129,116,81,363,53,130,78,360,117,50,127,79,361,118,48,128,80,362,119,49,126,370,112,57,73,122,371,113,58,74,120,369,111,59,72,121,366,108,56,76,125,367,109,54,77,123,368,110,55,75,124,670,674,678,684,328,35,376,87,290,88,329,33,377,288,34,89,327,375,289,86,324,31,372,293,84,325,32,373,291,85,326,30,374,292,334,26,382,93,296,335,24,383,94,294,333,25,381,95,295,330,29,378,92,299,331,27,379,90,297,332,28,380,91,298,672,667,671,679,404,159,316,100,352,101,406,160,317,353,161,99,402,315,351,96,396,158,312,348,97,398,156,313,349,98,400,157,314,350,417,165,322,106,358,419,166,323,107,359,415,167,321,105,357,409,164,318,102,354,411,162,319,103,355,413,163,320,104,356,662,676,681,668 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#9c565a9fd79b154e390f38dd387d90fedf9817e0675733b83815c4693870456f, 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 19:18:50 · history