Equation 677 Database

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Magma 3518404bcb73…

magma 3518404bcb73
Size
705
Isomorphism class hash
3518404bcb7357ec283b9d0f4097741a2dc621c5ff7d7a214c1691abb0885d8e
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 19:14:22
Display reorder
660,3,364,376,352,388,0,365,377,353,389,2,366,378,354,390,367,6,379,355,391,368,4,380,356,392,369,5,381,357,393,382,370,9,358,394,383,371,7,359,395,384,372,8,360,396,373,385,12,361,397,374,386,10,362,398,375,387,11,363,399,685,686,688,687,125,188,492,511,506,123,186,490,512,507,124,187,491,513,505,191,121,495,510,502,189,122,493,508,503,190,120,494,509,504,487,194,116,517,497,488,192,114,518,498,489,193,115,519,496,197,486,119,516,500,195,484,117,514,501,196,485,118,515,499,701,702,704,703,616,343,314,337,320,617,344,315,338,321,618,345,313,339,319,342,619,310,336,316,340,620,311,334,317,341,621,312,335,318,305,349,622,328,326,306,350,623,329,327,304,351,624,330,325,348,308,625,331,322,346,309,626,332,323,347,307,627,333,324,670,669,672,671,530,211,225,204,126,531,212,226,205,127,529,210,227,206,128,214,526,224,207,129,215,527,222,208,130,213,528,223,209,131,231,217,521,202,132,232,218,522,203,133,233,216,520,201,134,220,230,524,198,135,221,228,525,199,136,219,229,523,200,137,680,677,679,678,138,556,570,544,532,139,557,568,545,533,140,558,569,546,534,559,141,573,547,535,560,142,571,548,536,561,143,572,549,537,576,562,144,550,538,574,563,145,551,539,575,564,146,552,540,565,579,147,553,541,566,577,148,554,542,567,578,149,555,543,689,690,691,692,593,33,15,158,288,594,31,13,156,289,592,32,14,157,290,36,596,18,161,291,34,597,16,159,292,35,595,17,160,293,21,28,599,153,286,19,29,600,154,287,20,30,598,155,285,27,24,602,152,282,25,22,603,150,283,26,23,601,151,284,697,698,700,699,48,636,651,66,50,46,634,649,64,51,47,635,650,65,49,639,44,647,62,53,637,45,648,63,54,638,43,646,61,52,642,631,39,72,56,640,632,37,70,57,641,633,38,71,55,630,645,42,68,59,628,643,40,69,60,629,644,41,67,58,661,662,664,663,163,441,410,433,416,164,439,411,434,417,162,440,409,435,415,437,166,406,432,412,438,167,407,430,413,436,165,408,431,414,401,447,169,424,422,402,445,170,425,423,400,446,168,426,421,443,404,172,427,418,444,405,173,428,419,442,403,171,429,420,682,681,684,683,609,300,77,101,84,607,298,78,99,82,608,299,76,100,83,303,605,73,97,87,301,606,74,98,85,302,604,75,96,86,657,659,615,658,656,92,297,613,1,88,652,654,614,653,655,296,79,611,95,91,294,80,612,93,89,295,81,610,94,90,693,694,696,695,580,243,249,273,267,581,244,250,274,268,582,245,251,275,269,242,583,248,272,266,240,584,246,270,264,241,585,247,271,265,255,234,586,279,258,256,235,587,280,259,257,236,588,281,260,237,254,589,278,261,238,252,590,276,262,239,253,591,277,263,666,665,668,667,174,103,454,475,461,175,104,455,476,462,176,102,456,477,460,106,177,457,474,464,107,178,458,472,465,105,179,459,473,463,452,109,180,481,467,453,110,181,482,468,451,108,182,483,466,112,448,183,480,470,113,449,184,478,471,111,450,185,479,469,674,673,676,675 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#9613877152071542ba1176ebd2d9075b5c9b63b690264e2f5c72257d6a275b00, 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 19:14:23 · history