Equation 677 Database

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Magma 2f26161a26d5…

magma 2f26161a26d5
Size
705
Isomorphism class hash
2f26161a26d5337aded19213c10a83a2d4904c544eecea96c33c30ed1c700dee
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 19:47:43
Display reorder
660,52,410,40,613,606,53,408,41,614,607,39,51,612,608,409,413,48,36,616,609,411,37,49,617,610,412,50,38,615,611,58,46,416,619,604,59,47,414,620,605,57,45,415,618,603,42,54,419,622,600,43,55,417,623,601,44,56,418,621,602,687,688,686,685,470,217,248,210,253,468,218,246,211,254,247,469,212,252,216,220,473,251,213,256,221,249,471,214,257,219,472,250,215,255,476,243,223,208,259,474,244,224,209,260,475,245,222,207,258,242,479,226,204,262,240,477,227,205,263,241,478,225,206,261,703,704,701,702,119,588,403,582,74,117,589,404,583,72,402,118,584,73,590,591,115,406,585,77,592,407,116,586,75,593,114,405,587,76,110,401,594,580,80,108,399,595,581,78,109,400,596,579,79,397,113,597,576,83,398,111,598,577,81,396,112,599,578,82,671,672,670,669,176,488,492,286,269,174,486,493,287,267,494,175,285,268,487,491,179,495,282,265,489,496,177,283,266,490,178,497,284,264,171,498,483,277,275,172,499,484,278,273,173,500,485,276,274,501,170,482,280,271,502,168,480,281,272,503,169,481,279,270,679,680,678,677,299,510,151,197,187,297,511,152,195,188,150,298,196,186,512,513,295,154,193,190,514,155,296,194,191,515,294,153,192,189,290,149,508,203,185,288,147,509,201,183,289,148,507,202,184,145,293,504,199,181,146,291,505,200,182,144,292,506,198,180,692,691,690,689,331,555,96,541,534,332,556,97,542,535,98,330,540,536,557,554,334,99,544,537,552,100,335,545,538,553,333,101,543,539,329,102,561,547,532,327,103,562,548,533,328,104,563,546,531,105,325,560,550,528,106,326,558,551,529,107,324,559,549,530,699,700,698,697,23,128,133,11,67,21,126,134,9,68,132,22,10,66,127,131,19,136,7,70,129,137,20,8,71,130,18,135,6,69,14,139,123,2,65,12,140,124,1,63,13,138,125,0,64,142,17,122,5,61,143,15,120,3,62,141,16,121,4,60,663,664,662,661,626,343,352,426,363,624,344,353,427,364,351,625,428,365,342,346,629,348,429,362,347,349,627,430,360,345,628,350,431,361,632,358,341,424,369,630,359,339,425,370,631,357,340,423,371,354,635,337,420,368,355,633,338,421,366,356,634,336,422,367,682,683,684,681,571,648,649,651,650,572,652,653,655,654,656,570,659,658,657,645,574,644,647,646,636,637,575,638,639,640,573,641,643,642,569,382,372,394,385,567,383,373,395,386,568,381,374,393,384,378,565,375,390,388,379,566,376,391,389,380,564,377,392,387,695,696,693,694,520,163,307,24,315,521,164,308,25,316,306,519,26,317,162,166,516,310,27,314,167,311,517,28,312,165,518,309,29,313,526,305,161,30,321,527,303,159,31,322,525,304,160,32,323,301,522,157,33,320,302,523,158,34,318,300,524,156,35,319,667,668,665,666,95,461,239,445,440,93,459,237,446,438,238,94,444,439,460,457,91,235,448,443,458,236,92,449,441,456,90,234,447,442,86,230,467,451,435,84,228,465,452,436,85,229,466,450,437,233,89,463,454,434,231,87,464,455,432,232,88,462,453,433,675,676,673,674 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#aa12d1af20c50a7f712e8df2ac0f984d22557fb7db3e49cc75c20296525d3597, 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 19:47:44 · history