Equation 677 Database

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Magma 3754c3223e4f…

magma 3754c3223e4f
Size
705
Isomorphism class hash
3754c3223e4f671fb7a434e7a6bed9753e38e3689b5c75cdce368235b8d7b42c
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 16:44:11
Display reorder
660,593,344,108,352,175,345,594,109,353,176,343,595,107,354,174,104,596,340,355,171,597,105,341,356,172,342,106,357,598,173,350,114,358,591,166,115,351,359,592,167,113,349,360,590,165,346,110,361,587,169,347,111,362,588,170,348,112,363,589,168,665,663,671,662,185,502,246,205,387,503,183,247,206,385,504,184,248,204,386,245,188,505,201,383,186,243,506,202,384,507,244,203,187,382,500,237,211,180,378,238,501,212,181,376,239,499,210,182,377,496,240,207,179,381,497,241,208,177,379,498,242,209,178,380,690,688,685,687,73,430,303,130,119,431,74,301,128,120,432,75,302,129,121,299,76,433,133,118,77,300,434,131,116,435,298,132,78,117,428,294,136,71,125,292,429,134,72,126,293,427,135,70,127,424,297,139,67,124,425,295,137,68,122,426,296,138,69,123,667,670,666,664,401,255,195,526,398,256,402,196,527,399,257,400,197,528,397,198,404,258,529,394,405,199,259,530,395,260,200,531,403,396,253,193,524,407,389,194,254,525,408,390,192,252,523,406,388,249,189,520,410,392,250,190,521,411,393,251,191,522,409,391,673,679,674,676,514,562,271,86,418,563,515,272,87,419,564,516,270,88,420,267,517,565,89,421,518,268,566,90,422,567,269,91,519,423,560,262,84,512,416,263,561,85,513,417,261,559,83,511,415,556,265,80,508,412,557,266,81,509,413,558,264,82,510,414,661,672,668,669,369,45,164,53,538,46,367,162,51,539,47,368,163,52,540,160,365,44,49,541,366,161,42,50,542,43,159,48,364,543,36,155,59,375,536,153,37,57,373,537,154,38,58,374,535,39,158,55,371,532,40,156,56,372,533,41,157,54,370,534,696,698,697,693,568,629,98,79,146,643,642,99,641,640,647,646,100,645,644,101,650,651,649,648,654,102,655,653,652,659,103,657,658,656,627,96,147,574,144,97,628,148,572,145,95,626,149,573,143,623,92,150,570,140,624,93,151,571,141,625,94,152,569,142,702,701,703,704,60,478,29,273,442,479,630,27,631,443,480,632,28,633,444,25,635,481,634,445,637,26,482,636,446,483,24,638,639,447,476,35,277,66,440,33,477,278,64,441,34,475,279,65,439,472,31,276,62,436,473,32,274,63,437,474,30,275,61,438,694,699,700,695,581,214,338,236,550,215,582,339,234,551,213,583,337,235,552,334,584,217,232,553,585,335,218,233,554,216,336,231,586,555,220,329,227,579,548,330,221,225,580,549,328,219,226,578,547,223,332,230,575,544,224,333,228,576,545,222,331,229,577,546,680,682,681,684,605,490,19,288,454,491,606,20,286,455,492,607,18,287,456,22,608,493,291,457,609,23,494,289,458,495,21,290,610,459,488,17,283,603,452,15,489,284,604,453,16,487,285,602,451,484,13,282,599,448,485,14,280,600,449,486,12,281,601,450,677,675,683,678,617,466,7,311,320,467,618,8,312,321,468,619,6,310,319,10,620,469,314,316,621,11,470,315,317,471,9,313,622,318,464,5,309,615,326,3,465,307,616,327,4,463,308,614,325,460,0,305,611,322,461,2,306,612,323,462,1,304,613,324,689,691,692,686 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#3c7860e7d36dbffc79bc7c2d0a8ff0a692ab326401712ae14ddffd4858b8cd98, 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 16:44:12 · history