Equation 677 Database

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Magma 03e4de333141…

magma 03e4de333141
Size
705
Isomorphism class hash
03e4de333141ba590df15678d911e19203b2315d14d2ccd922c9f2c29d721a6b
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 16:21:34
Display reorder
704,126,150,165,143,127,141,151,166,128,142,152,167,139,129,153,164,140,130,154,162,138,131,155,163,156,148,124,134,157,149,125,132,158,147,123,133,144,159,120,137,145,160,121,135,146,161,122,136,174,175,176,177,178,179,172,173,170,168,169,171,683,680,682,681,580,30,5,13,581,14,31,3,579,12,32,4,16,576,33,0,17,577,34,2,15,578,35,1,11,28,586,19,9,29,587,20,10,27,585,18,24,7,582,22,25,8,583,23,26,6,584,21,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,507,217,235,209,508,207,218,236,509,208,216,234,205,506,220,238,206,504,221,239,204,505,219,237,233,223,513,215,231,224,514,213,232,222,515,214,226,229,512,211,227,230,510,212,225,228,511,210,193,194,192,196,197,195,199,200,201,202,203,198,669,671,668,670,51,423,438,408,52,409,424,439,53,410,425,440,411,50,422,441,412,48,420,442,413,49,421,443,436,429,57,414,437,430,58,415,435,431,59,416,428,432,56,417,426,433,54,418,427,434,55,419,449,447,448,445,446,444,455,453,450,451,452,454,679,676,678,677,296,541,560,533,294,531,542,558,295,532,540,559,529,299,544,563,530,297,545,561,528,298,543,562,555,547,291,539,556,548,292,537,557,546,293,538,550,554,290,535,551,552,288,536,549,553,289,534,568,569,567,564,565,566,574,575,572,570,571,573,689,690,688,691,638,311,318,343,636,344,309,319,637,342,310,320,346,641,307,321,347,639,308,322,345,640,306,323,316,302,644,341,317,300,642,339,315,301,643,340,305,312,647,337,303,313,645,338,304,314,646,336,329,327,328,325,326,324,335,333,330,331,332,334,692,694,693,695,527,241,260,278,525,276,242,258,526,277,240,259,281,523,244,263,279,524,245,261,280,522,243,262,255,247,518,284,256,248,516,282,257,246,517,283,250,254,521,287,251,252,519,285,249,253,520,286,268,269,267,264,265,266,274,275,272,270,271,273,661,662,660,663,71,384,351,377,69,375,385,352,70,376,386,353,373,67,387,350,374,68,388,348,372,66,389,349,357,390,62,383,358,391,60,381,359,392,61,382,393,356,65,379,394,354,63,380,395,355,64,378,361,362,360,364,365,363,367,368,369,370,371,366,685,686,684,687,399,92,107,73,400,74,90,105,401,72,91,106,76,398,95,103,77,396,93,104,75,397,94,102,98,87,405,79,96,88,406,80,97,89,407,78,86,101,404,82,84,99,402,83,85,100,403,81,108,109,110,111,112,113,114,115,119,117,118,116,698,697,699,696,189,457,476,493,190,494,458,474,191,492,456,475,496,188,460,479,497,186,461,477,495,187,459,478,471,463,180,499,472,464,181,500,473,462,182,498,466,470,183,502,467,468,184,503,465,469,185,501,484,485,483,480,481,482,490,491,488,486,487,489,666,665,667,664,46,620,634,611,47,609,618,635,45,610,619,633,607,42,623,630,608,43,621,631,606,44,622,632,625,615,37,602,626,616,38,600,624,617,36,601,614,628,40,605,612,629,41,603,613,627,39,604,590,588,589,593,591,592,596,594,598,599,597,595,674,673,675,672 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#2e8e4ac0a437874a6303a2bb1c968f3f1df955f15fe5de36e1349d884d5d267c, 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 16:21:35 · history