Equation 677 Database

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Magma dc2de6e31647…

magma dc2de6e31647
Size
705
Isomorphism class hash
dc2de6e31647f16d462e702069d0fde31faafec635e0de29abd1b3c9734f2e6c
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 17:33:42
Display reorder
660,208,603,613,594,334,209,335,604,614,595,207,333,605,612,596,204,602,330,616,597,205,600,331,617,598,206,601,332,615,599,619,214,609,340,592,215,610,341,620,593,213,611,339,618,591,608,210,336,622,588,606,211,337,623,589,607,212,338,621,590,687,688,686,685,407,51,62,37,27,405,28,52,60,38,406,29,53,61,36,403,50,26,65,40,404,48,24,63,41,402,49,25,64,39,68,413,57,33,43,411,58,34,66,44,412,59,35,67,42,56,409,32,71,46,54,410,30,69,47,55,408,31,70,45,703,704,701,702,318,558,568,192,576,319,577,559,569,193,320,578,560,567,194,321,561,579,564,195,322,562,580,565,196,323,563,581,566,197,574,324,556,582,198,325,557,583,575,199,326,555,584,573,200,552,327,585,570,201,553,328,586,571,202,554,329,587,572,203,671,672,670,669,75,461,425,449,437,76,435,459,423,447,77,436,460,424,448,74,457,433,421,445,72,458,434,422,446,73,456,432,420,444,416,81,452,428,440,82,450,426,414,438,83,451,427,415,439,455,80,431,419,443,453,78,429,417,441,454,79,430,418,442,679,680,678,677,155,496,507,485,473,153,471,497,508,483,154,472,495,509,484,151,492,469,506,481,152,493,470,504,482,150,494,468,505,480,498,146,487,464,476,144,488,462,499,474,145,486,463,500,475,490,149,467,501,479,491,147,465,502,477,489,148,466,503,478,692,691,690,689,4,530,179,304,294,5,295,528,177,305,3,296,529,178,303,1,533,297,175,300,0,531,298,176,301,2,532,299,174,302,170,10,525,292,310,11,526,293,168,311,9,527,291,169,309,524,6,288,173,306,522,7,289,171,307,523,8,290,172,308,699,700,698,697,124,229,244,223,134,125,132,230,245,224,123,133,228,243,222,120,232,137,240,226,121,233,135,241,227,122,231,136,242,225,250,130,235,140,221,131,236,138,251,219,129,234,139,249,220,238,126,143,246,217,239,127,141,247,218,237,128,142,248,216,663,664,662,661,626,367,85,357,348,624,349,368,86,358,625,350,366,84,359,629,370,351,88,356,627,371,352,89,354,628,369,353,87,355,91,632,373,346,363,630,374,347,92,364,631,372,345,90,365,376,635,342,94,362,377,633,343,95,360,375,634,344,93,361,682,683,684,681,184,648,651,649,650,185,654,653,655,652,183,658,657,659,656,180,644,646,647,645,181,637,636,638,639,182,640,642,643,641,550,190,541,539,315,191,542,537,551,316,189,540,538,549,317,544,186,535,546,314,545,187,536,547,312,543,188,534,548,313,695,696,693,694,515,279,162,266,259,513,260,280,163,264,514,258,281,164,265,511,278,262,165,269,512,276,263,166,267,510,277,261,167,268,160,521,285,257,272,519,286,255,161,270,520,287,256,159,271,284,517,253,156,275,282,518,254,157,273,283,516,252,158,274,667,668,665,666,16,110,384,100,395,17,393,108,385,101,15,394,109,386,99,12,113,391,387,96,13,111,392,388,97,14,112,390,389,98,382,22,116,401,106,23,114,399,383,107,21,115,400,381,105,119,18,397,378,102,117,19,398,379,103,118,20,396,380,104,675,676,673,674 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#58f4898eb0f0372a4c749060353e7621900aa789e1d944064f9989e660cee0fd, 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 17:33:44 · history