Equation 677 Database

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Magma 5652d3d2ed4f…

magma 5652d3d2ed4f
Size
705
Isomorphism class hash
5652d3d2ed4fbb32145ca3d9b8064cd4bb99ac6033590241a6e9453b5bf820ec
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 16:52:11
Display reorder
660,345,59,31,477,501,346,57,502,32,478,500,58,344,30,476,341,55,497,34,473,342,56,498,35,474,343,54,499,33,475,492,50,29,336,468,493,48,27,337,469,491,49,28,335,467,53,495,25,339,471,51,496,26,340,472,52,494,24,338,470,661,672,667,668,489,583,113,381,200,490,584,201,114,382,202,582,488,115,380,485,579,199,116,377,486,580,197,117,378,487,581,198,118,379,191,574,111,480,372,192,575,112,481,373,193,573,110,479,371,577,194,107,483,375,578,195,108,484,376,576,196,109,482,374,688,690,686,685,525,369,308,504,429,526,370,430,309,505,428,368,524,310,503,521,365,425,307,507,522,366,426,305,508,523,367,427,306,506,420,360,299,516,510,421,361,300,517,511,419,359,301,515,509,363,423,302,519,513,364,424,303,520,514,362,422,304,518,512,669,663,670,665,205,465,150,405,619,203,466,620,151,406,618,464,204,149,404,208,461,615,153,401,206,462,616,154,402,207,463,617,152,403,610,456,148,211,396,611,457,146,209,397,609,455,147,210,395,459,613,144,214,399,460,614,145,212,400,458,612,143,213,398,680,676,674,681,393,441,130,163,607,394,442,608,128,161,606,440,392,129,162,389,437,603,126,166,390,438,604,127,164,391,439,605,125,165,598,432,121,384,158,599,433,119,385,159,597,431,120,383,160,435,601,124,387,157,436,602,122,388,155,434,600,123,386,156,664,666,662,671,357,287,20,548,284,358,288,285,18,549,286,289,356,19,547,353,290,283,23,544,354,291,281,21,545,355,292,282,22,546,275,293,15,348,539,276,294,16,349,540,277,295,17,347,538,296,278,14,351,542,297,279,12,352,543,298,280,13,350,541,699,694,697,693,537,572,36,655,79,657,659,658,37,656,78,571,536,38,654,533,568,82,39,651,534,569,80,40,652,535,570,81,41,653,77,563,42,528,646,75,564,43,529,647,76,562,44,527,645,566,73,45,531,649,567,74,46,532,650,565,72,47,530,648,703,704,702,701,560,631,178,131,417,561,632,418,176,132,416,630,559,177,133,556,627,413,174,134,557,628,414,175,135,558,629,415,173,136,408,622,169,551,137,409,623,167,552,138,407,621,168,550,139,625,411,172,554,140,626,412,170,555,141,624,410,171,553,142,698,700,696,695,268,239,334,255,236,266,240,237,332,256,238,241,267,333,254,264,242,235,330,251,265,243,233,331,252,263,244,234,329,253,227,245,325,274,261,228,246,323,272,262,229,247,324,273,260,248,230,328,270,257,249,231,326,271,258,250,232,327,269,259,682,675,684,673,643,185,94,106,0,644,186,2,92,104,1,187,642,93,105,639,188,4,90,102,640,189,5,91,103,641,190,3,89,101,7,183,85,634,97,8,184,83,635,95,6,182,84,633,96,179,10,88,637,100,180,11,86,638,98,181,9,87,636,99,683,677,679,678,595,453,321,219,67,596,454,68,322,220,66,452,594,320,218,591,449,70,317,215,592,450,71,318,216,593,451,69,319,217,65,444,312,586,225,63,445,313,587,226,64,443,311,585,224,447,61,315,589,221,448,62,316,590,222,446,60,314,588,223,691,687,692,689 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#41328e14760452489c50b79fcc49c074869181cbfbd0a816da081f28123ef346, 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 16:52:12 · history