Equation 677 Database

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Magma 1217c083f20b…

magma 1217c083f20b
Size
705
Isomorphism class hash
1217c083f20b4813cae16a08772d0102d1111fc32e0af5a6667c3915c33c5d73
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 21:51:03
Display reorder
660,145,595,578,63,51,579,593,64,146,52,144,594,580,65,53,591,148,581,62,50,592,149,582,60,48,590,147,583,61,49,576,586,69,151,57,577,584,70,152,58,575,585,71,150,59,589,572,68,154,56,587,573,66,155,54,588,574,67,153,55,687,688,686,685,326,353,386,381,360,384,351,382,324,361,325,352,385,383,362,349,329,389,380,363,350,327,387,378,364,348,328,388,379,365,392,359,372,332,366,390,357,373,330,367,391,358,374,331,368,355,395,375,335,369,356,393,376,333,370,354,394,377,334,371,703,704,701,702,139,553,537,533,560,538,551,534,140,561,138,552,536,535,562,549,142,540,532,563,550,143,541,530,564,548,141,539,531,565,543,559,524,137,566,544,557,525,135,567,542,558,526,136,568,555,546,527,133,569,556,547,528,134,570,554,545,529,132,571,671,672,670,669,221,423,411,404,436,412,424,402,222,437,223,425,413,403,435,422,220,410,407,432,420,218,408,405,433,421,219,409,406,434,417,429,399,227,442,418,430,400,228,443,419,431,401,229,441,428,416,398,226,438,426,414,396,224,439,427,415,397,225,440,679,680,678,677,454,237,91,258,243,92,238,259,455,244,453,236,90,257,242,240,450,94,254,246,241,451,95,255,247,239,452,93,256,245,89,235,264,445,249,87,233,265,446,250,88,234,263,444,248,231,85,260,448,252,232,86,261,449,253,230,84,262,447,251,692,691,690,689,197,99,111,281,512,112,100,282,195,510,196,101,113,283,511,98,193,110,280,515,96,194,108,278,513,97,192,109,279,514,117,105,287,203,507,118,106,288,201,508,119,107,289,202,509,104,116,286,199,506,102,114,284,200,504,103,115,285,198,505,699,700,698,697,3,17,78,45,24,79,15,46,4,25,5,16,80,47,26,13,2,81,44,27,14,1,82,42,28,12,0,83,43,29,76,23,36,9,30,77,21,37,10,31,75,22,38,11,32,19,72,39,8,33,20,73,40,6,34,18,74,41,7,35,663,664,662,661,158,603,634,629,608,632,604,630,156,609,157,602,633,631,610,606,161,637,628,611,607,159,635,626,612,605,160,636,627,613,640,601,620,164,614,638,599,621,162,615,639,600,622,163,616,597,643,623,167,617,598,641,624,165,618,596,642,625,166,619,682,683,684,681,121,659,658,657,656,650,651,649,122,648,120,655,654,653,652,522,124,297,299,204,646,125,644,645,647,523,123,296,298,211,295,520,217,127,207,293,521,215,128,205,294,519,216,126,206,516,291,213,130,210,517,292,214,131,208,518,290,212,129,209,695,696,693,694,272,457,496,481,473,497,458,482,273,471,274,456,495,480,472,460,275,492,484,469,461,276,493,485,470,459,277,494,483,468,502,463,487,270,479,503,464,488,271,477,501,462,486,269,478,466,498,490,266,475,467,499,491,267,476,465,500,489,268,474,667,668,665,666,341,184,176,317,308,174,185,315,339,306,340,183,175,316,307,180,337,179,313,311,181,338,177,314,309,182,336,178,312,310,171,190,323,347,303,172,191,321,345,304,173,189,322,346,305,186,170,319,343,302,187,168,320,344,300,188,169,318,342,301,675,676,673,674 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#f6b6fc56ae6a00548325e9d66bb78aa16bb0852529ebdb9883eeafc26b8a7eae, 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 21:51:04 · history