Equation 677 Database

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Magma 5d12cd6415b7…

magma 5d12cd6415b7
Size
705
Isomorphism class hash
5d12cd6415b742ba59c6ad0e9f9c7c58259d7dee06530bf5a83d314511ddd62c
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 19:45:13
Display reorder
660,64,85,345,224,354,65,222,86,346,355,63,223,84,347,356,81,67,348,220,353,68,82,349,221,351,66,83,350,219,352,70,76,343,230,360,77,71,344,228,361,69,75,342,229,362,79,73,339,226,359,80,74,340,227,357,78,72,341,225,358,685,686,688,687,258,126,136,429,37,259,430,127,137,38,260,431,128,135,36,125,257,139,432,33,255,123,140,433,34,256,124,138,434,35,264,132,142,427,28,133,265,143,428,29,266,134,141,426,27,131,263,145,423,31,129,261,146,424,32,130,262,144,425,30,701,702,704,703,337,94,571,218,586,338,216,95,572,587,336,217,93,570,585,97,333,574,214,582,334,98,575,215,583,335,96,573,213,584,328,92,569,209,577,90,329,567,207,578,327,91,568,208,576,88,331,565,212,580,89,332,566,210,581,87,330,564,211,579,670,669,672,671,272,459,472,447,440,270,448,460,473,438,271,449,461,471,439,462,268,475,450,436,269,463,476,451,437,267,464,474,452,435,278,465,478,453,446,466,276,479,454,444,277,467,477,455,445,468,274,481,456,442,469,275,482,457,443,470,273,480,458,441,680,677,679,678,282,42,51,489,23,283,490,43,52,21,284,491,44,53,22,41,281,54,492,26,279,39,55,493,24,280,40,56,494,25,288,48,57,487,18,49,289,58,488,19,290,50,59,486,20,47,287,60,483,17,45,285,61,484,15,46,286,62,485,16,689,690,691,692,309,176,8,170,549,310,168,174,6,550,311,169,175,7,551,172,312,4,166,552,313,173,5,167,553,314,171,3,165,554,307,182,14,161,547,180,308,12,159,548,306,181,13,160,546,178,303,10,164,543,179,304,11,162,544,177,305,9,163,545,697,698,700,699,599,633,647,613,605,597,614,634,645,603,598,612,635,646,604,632,595,643,616,601,596,630,644,617,602,594,631,642,615,600,590,624,638,619,611,625,588,636,620,609,589,626,637,618,610,627,593,641,622,607,628,591,639,623,608,629,592,640,621,606,661,662,664,663,242,404,369,389,378,240,387,402,370,379,241,388,403,371,380,400,238,372,392,377,239,401,373,390,375,237,399,374,391,376,233,410,367,395,384,408,231,368,393,385,232,409,366,394,386,406,236,363,398,383,407,234,364,396,381,405,235,365,397,382,682,681,684,683,324,559,183,198,189,325,199,560,184,190,326,200,558,185,191,562,323,186,197,192,321,563,187,195,193,322,561,188,196,194,315,655,652,654,653,659,316,656,658,657,317,650,649,648,651,556,318,204,203,0,557,319,205,201,2,555,320,206,202,1,693,694,696,695,295,519,533,507,495,296,508,520,531,496,294,509,521,532,497,522,291,536,510,498,292,523,534,511,499,293,524,535,512,500,301,525,539,513,501,526,302,537,514,502,300,527,538,515,503,528,297,542,516,504,529,298,540,517,505,530,299,541,518,506,666,665,668,667,417,108,155,251,121,418,249,109,153,122,419,250,110,154,120,107,420,158,254,117,421,105,156,252,118,422,106,157,253,119,415,99,150,246,112,100,416,151,247,113,414,101,152,248,111,102,411,149,245,115,103,412,147,243,116,104,413,148,244,114,674,673,676,675 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#a72914db9cdb367a789c5baa8372a3d5fedd55bc0a2411348ad61481f273a706, 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 19:45:14 · history