Equation 677 Database

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Magma aaf01e35cc1b…

magma aaf01e35cc1b
Size
705
Isomorphism class hash
aaf01e35cc1ba652ae7c6521800d1c43455ca035bfb8d8b354512b554ee5e9a3
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 18:19:44
Display reorder
660,134,108,454,8,226,135,106,452,9,227,7,107,133,453,228,130,111,450,4,229,131,109,451,5,230,132,110,449,6,231,103,460,125,14,224,104,458,126,15,225,105,459,124,13,223,456,102,128,10,220,457,100,129,11,221,455,101,127,12,222,667,672,664,665,465,337,382,442,165,466,335,380,440,163,441,336,464,381,164,461,340,378,438,161,462,338,379,439,162,463,339,377,437,160,332,388,471,448,171,333,386,472,446,169,334,387,470,447,170,384,331,467,444,167,385,329,468,445,168,383,330,469,443,166,685,687,689,686,430,156,255,592,514,428,154,253,590,512,591,155,429,254,513,426,159,251,588,510,427,157,252,589,511,425,158,250,587,509,151,246,436,598,520,152,244,434,596,518,153,245,435,597,519,249,150,432,594,516,247,148,433,595,517,248,149,431,593,515,668,671,663,670,478,350,568,177,502,476,351,566,175,500,176,352,477,567,501,474,349,564,173,498,475,347,565,174,499,473,348,563,172,497,341,574,484,183,508,342,572,482,181,506,343,573,483,182,507,570,344,480,179,504,571,345,481,180,505,569,346,479,178,503,678,683,677,681,189,77,544,490,358,187,78,542,488,356,489,76,188,543,357,185,80,540,486,354,186,81,541,487,355,184,79,539,485,353,83,550,195,496,364,84,548,193,494,362,82,549,194,495,363,546,86,191,492,360,547,87,192,493,361,545,85,190,491,359,661,666,662,669,123,138,413,526,233,121,136,414,524,234,525,137,122,415,232,119,141,416,522,236,120,139,417,523,237,118,140,418,521,235,144,419,114,532,239,142,420,112,530,240,143,421,113,531,238,422,147,117,528,242,423,145,115,529,243,424,146,116,527,241,695,696,694,693,635,46,632,633,634,627,47,626,624,625,629,48,631,628,630,599,49,536,534,0,600,50,537,535,2,601,51,538,533,3,44,657,659,656,658,45,648,651,649,650,43,653,655,652,654,641,40,643,640,642,645,41,647,644,646,637,42,639,636,638,704,701,703,702,308,92,18,59,312,309,93,16,60,313,58,91,310,17,311,307,88,21,62,315,305,89,19,63,316,306,90,20,61,314,98,24,622,57,623,99,22,618,55,619,97,23,620,56,621,27,94,614,53,615,25,95,616,54,617,26,96,304,52,1,699,697,700,698,607,209,580,297,394,605,210,578,295,392,296,208,606,579,393,603,212,576,293,390,604,213,577,294,391,602,211,575,292,389,215,586,613,303,400,216,584,611,301,398,214,585,612,302,399,582,218,609,299,396,583,219,610,300,397,581,217,608,298,395,675,674,684,682,369,33,328,406,556,370,31,326,404,554,405,32,368,327,555,365,29,324,402,552,366,30,325,403,553,367,28,323,401,551,39,319,375,412,562,37,317,376,410,560,38,318,374,411,561,322,35,371,408,558,320,36,372,409,559,321,34,373,407,557,680,676,679,673,263,66,270,284,204,264,64,268,285,202,283,65,262,269,203,266,69,273,280,207,267,67,271,281,205,265,68,272,282,206,72,276,261,290,199,70,274,259,291,200,71,275,260,289,201,279,75,257,286,198,277,73,258,287,196,278,74,256,288,197,690,691,688,692 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#7b2d22e166b1ff02dad840b7a1389a143f850a338adb3bda964b6fc81ff7fb8b, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 18:19:44 · history