Equation 677 Database

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Magma 720cc6fd5045…

magma 720cc6fd5045
Size
705
Isomorphism class hash
720cc6fd504542e6e724ce861d2d2e78dd41c50e89bd2e809852adbec00dbe4c
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 21:08:49
Display reorder
660,196,130,452,512,64,197,131,450,510,65,195,129,451,511,63,133,199,448,508,67,134,200,449,509,68,132,198,447,507,66,202,458,128,518,70,203,456,126,516,71,201,457,127,517,69,454,205,124,514,73,455,206,125,515,74,453,204,123,513,72,671,669,667,662,318,275,114,440,246,319,273,115,438,247,320,274,116,439,248,278,317,113,436,245,276,315,111,437,243,277,316,112,435,244,324,120,270,446,252,325,121,271,444,253,326,122,272,445,254,119,323,269,442,251,117,321,267,443,249,118,322,268,441,250,688,686,690,689,88,154,230,161,587,89,155,228,159,585,87,153,229,160,586,157,91,226,164,583,158,92,227,162,584,156,90,225,163,582,94,221,152,167,593,95,219,150,165,591,93,220,151,166,592,224,97,148,170,589,222,98,149,168,590,223,96,147,169,588,672,666,665,664,332,284,541,542,19,330,282,538,537,20,331,283,540,539,18,280,328,533,534,15,281,329,535,536,16,279,327,531,532,17,338,553,290,554,25,336,550,288,549,26,337,551,289,552,24,545,334,286,546,21,547,335,287,548,22,544,333,285,543,23,684,681,682,674,340,368,476,296,28,341,366,474,294,29,339,367,475,295,27,364,343,472,292,31,365,344,473,293,32,363,342,471,291,30,346,482,374,302,34,347,480,372,300,35,345,481,373,301,33,478,349,370,298,37,479,350,371,299,38,477,348,369,297,36,670,661,668,663,80,214,392,144,9,78,215,390,145,10,79,213,391,146,11,217,76,388,143,12,218,77,389,141,13,216,75,387,142,14,86,398,212,135,7,84,396,210,136,8,85,397,211,137,6,394,82,208,138,3,395,83,209,139,4,393,81,207,140,5,696,697,695,693,58,635,634,633,632,59,627,626,625,624,57,631,630,629,628,594,61,595,0,556,596,62,597,2,557,598,60,599,1,555,56,659,658,656,657,54,651,650,648,649,55,655,654,652,653,643,52,642,640,641,647,53,646,644,645,639,51,638,636,637,701,702,703,704,42,356,563,611,610,43,354,561,606,607,44,355,562,608,609,352,41,559,602,603,353,39,560,605,604,351,40,558,600,601,48,569,362,623,622,49,567,360,618,619,50,568,361,620,621,565,47,358,614,615,566,45,359,617,616,564,46,357,612,613,699,700,698,694,183,524,575,500,416,184,522,573,498,414,185,523,574,499,415,520,186,571,496,412,521,187,572,497,413,519,188,570,495,411,189,581,530,506,422,190,579,528,504,420,191,580,529,505,421,577,192,526,502,418,578,193,527,503,419,576,194,525,501,417,676,679,683,680,260,310,464,428,380,258,311,462,426,378,259,309,463,427,379,313,256,460,424,376,314,257,461,425,377,312,255,459,423,375,266,470,308,434,386,264,468,306,432,384,265,469,307,433,385,466,262,304,430,382,467,263,305,431,383,465,261,303,429,381,675,677,678,673,407,239,109,488,181,405,237,110,486,182,406,238,108,487,180,242,410,105,484,177,240,408,106,485,178,241,409,107,483,179,402,100,234,494,172,403,101,235,492,173,404,99,236,493,171,103,401,233,490,175,104,399,231,491,176,102,400,232,489,174,685,687,691,692 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#d958d834958932013e293186c3edbca2299f39c5df5a243bf65f8d4f2fad3f22, 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 21:08:50 · history