Equation 677 Database

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Magma 2a3d170ad500…

magma 2a3d170ad500
Size
705
Isomorphism class hash
2a3d170ad50090b9bb9e8a1783218ffb80c8b17c6946e2e556e0e0e7dad9a748
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 21:12:16
Display reorder
660,73,366,23,27,352,74,21,28,353,367,72,368,22,29,351,76,19,365,26,355,77,20,363,24,356,75,18,364,25,354,14,79,357,33,350,34,12,80,358,348,13,78,359,35,349,82,17,360,32,346,83,15,361,30,347,81,16,362,31,345,685,686,688,687,0,437,146,113,107,2,144,111,105,435,1,436,145,112,106,4,149,440,109,103,5,147,438,110,104,3,148,439,108,102,152,7,432,119,98,117,150,8,433,96,151,6,434,118,97,10,155,431,115,101,11,153,429,116,99,9,154,430,114,100,701,702,704,703,67,331,333,265,576,68,334,263,574,332,66,330,335,264,575,70,336,327,261,579,71,337,328,262,577,69,338,329,260,578,339,65,322,256,571,254,340,63,323,572,341,64,321,255,573,61,342,325,259,570,62,343,326,257,568,60,344,324,258,569,670,669,672,671,130,448,464,470,479,131,462,468,477,449,129,447,463,469,478,126,460,451,466,482,127,461,452,467,480,128,459,450,465,481,455,121,446,476,485,474,453,122,444,483,454,120,445,475,484,124,458,442,472,488,125,456,443,473,486,123,457,441,471,487,680,677,679,678,36,141,495,277,282,37,496,275,283,142,38,143,497,276,281,39,498,140,273,278,40,499,138,274,279,41,500,139,272,280,493,42,132,268,288,266,494,43,133,289,492,44,134,267,287,45,489,135,271,284,46,490,136,269,285,47,491,137,270,286,689,690,691,692,305,211,226,229,557,306,227,230,555,212,307,210,225,228,556,304,222,214,232,560,302,223,215,233,558,303,224,213,231,559,217,311,209,235,552,236,218,312,207,553,216,313,208,234,554,310,220,205,238,551,308,221,206,239,549,309,219,204,237,550,697,698,700,699,581,620,639,597,605,582,637,595,606,621,580,619,638,596,604,584,635,616,593,608,585,636,617,594,609,583,634,618,592,607,630,587,626,603,611,601,628,588,627,612,629,586,625,602,610,590,633,622,599,614,591,631,623,600,615,589,632,624,598,613,661,662,664,663,84,372,384,397,416,85,385,398,414,373,86,374,386,396,415,87,383,371,393,412,88,381,369,394,413,89,382,370,395,411,390,90,378,403,407,404,391,91,379,405,392,92,380,402,406,93,389,377,399,410,94,387,375,400,408,95,388,376,401,409,682,681,684,683,59,246,250,564,319,57,251,562,320,244,58,245,252,563,318,55,249,242,567,315,56,247,243,565,316,54,248,241,566,317,645,50,644,647,646,561,253,48,240,314,640,49,641,642,643,53,656,657,659,658,51,648,649,651,650,52,652,653,655,654,693,694,696,695,299,539,504,516,530,300,505,517,528,537,301,538,506,518,529,298,503,542,515,526,296,501,540,513,527,297,502,541,514,525,510,290,545,522,536,523,511,291,543,534,512,292,544,524,535,293,509,548,521,532,294,507,546,519,533,295,508,547,520,531,666,665,668,667,418,168,180,194,161,419,181,192,159,169,417,170,182,193,160,421,183,171,197,157,422,184,172,195,158,420,185,173,196,156,186,424,174,200,167,198,187,425,175,165,188,423,176,199,166,427,189,177,203,163,428,190,178,201,164,426,191,179,202,162,674,673,676,675 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#dd5d8cb242321da00ce62fc2d476849be658b6b0a3d2fd229095425016dc303c, 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 21:12:17 · history