Equation 677 Database

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Magma 33a16b85dc30…

magma 33a16b85dc30
Size
705
Isomorphism class hash
33a16b85dc3003d998c11b14c167904a93303f8cbbe51cdf568e7992f4d7b7e2
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 19:46:56
Display reorder
704,191,139,173,161,189,140,171,159,190,138,172,160,187,142,169,157,188,143,170,158,186,141,168,156,137,182,167,179,135,180,165,177,136,181,166,178,133,185,163,175,134,183,164,176,132,184,162,174,146,144,145,149,147,148,152,150,154,155,153,151,683,680,682,681,23,41,549,537,21,39,550,538,22,40,551,539,19,37,548,536,20,38,546,534,18,36,547,535,47,14,528,540,45,12,529,541,46,13,530,542,43,17,531,543,44,15,532,544,42,16,533,545,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,423,27,415,404,424,28,416,402,425,29,414,403,422,26,418,407,420,24,419,405,421,25,417,406,33,429,399,413,34,430,400,411,35,431,401,412,32,428,398,409,30,426,396,410,31,427,397,408,394,395,393,390,391,392,385,386,387,388,389,384,669,671,668,670,363,69,356,343,364,70,354,344,365,71,355,342,362,68,359,346,360,66,357,347,361,67,358,345,60,369,341,351,61,370,339,352,62,371,340,353,63,368,337,350,64,366,338,348,65,367,336,349,335,333,334,331,332,330,326,324,328,329,327,325,679,676,678,677,505,240,501,489,506,241,502,490,504,242,503,491,508,243,500,488,509,244,498,486,507,245,499,487,246,511,480,492,247,512,481,493,248,510,482,494,249,514,483,495,250,515,484,496,251,513,485,497,525,526,527,524,522,523,516,517,521,519,520,518,689,690,688,691,623,263,605,638,621,261,603,636,622,262,604,637,619,259,601,641,620,260,602,639,618,258,600,640,254,614,644,611,252,612,642,609,253,613,643,610,257,617,647,607,255,615,645,608,256,616,646,606,629,627,628,625,626,624,635,633,630,631,632,634,692,694,693,695,445,6,442,476,446,7,443,474,444,8,441,475,448,9,438,479,449,10,439,477,447,11,440,478,4,451,471,433,5,452,472,434,3,450,473,432,1,454,470,436,0,455,468,437,2,453,469,435,465,466,467,464,462,463,456,457,461,459,460,458,661,662,660,663,292,80,283,271,293,78,284,272,291,79,282,270,288,83,286,274,289,81,287,275,290,82,285,273,75,298,269,281,76,299,267,279,77,297,268,280,74,294,265,277,72,295,266,278,73,296,264,276,306,307,308,309,310,311,304,305,302,300,301,303,685,686,684,687,101,318,90,129,99,319,91,130,100,320,92,131,97,321,93,128,98,322,94,126,96,323,95,127,316,107,120,88,317,105,121,89,315,106,122,87,312,103,123,84,313,104,124,85,314,102,125,86,115,116,114,118,119,117,113,111,108,109,110,112,698,697,699,696,210,379,193,232,211,380,194,233,212,378,192,231,213,382,196,228,214,383,197,229,215,381,195,230,377,208,238,199,375,209,239,200,376,207,237,198,373,204,234,202,374,205,235,203,372,206,236,201,216,217,218,219,220,221,222,223,227,225,226,224,666,665,667,664,560,53,593,581,558,51,591,579,559,52,592,580,563,49,589,577,561,50,590,578,562,48,588,576,59,555,587,599,57,556,585,597,58,557,586,598,55,554,583,595,56,552,584,596,54,553,582,594,566,564,565,569,567,568,572,570,574,575,573,571,674,673,675,672 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#a9f62e2491236cd33b6e554b1a4dc1a2938062e1ffa7bd655365fbe4324c4209, 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 19:46:57 · history