Equation 677 Database

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Magma 664916ac74cb…

magma 664916ac74cb
Size
705
Isomorphism class hash
664916ac74cb407e630f2f20a2cbc46158cd64773a5e774cdabf233e42787577
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 17:32:25
Display reorder
660,350,342,452,225,386,348,343,450,226,384,349,344,451,227,385,345,353,455,224,389,346,351,453,222,387,347,352,454,223,388,340,356,216,458,392,341,354,217,456,390,339,355,218,457,391,359,336,219,461,395,357,337,220,459,393,358,338,221,460,394,666,663,662,661,294,70,166,58,148,295,71,167,59,149,296,69,165,57,147,66,297,162,54,144,67,298,163,55,145,68,299,164,56,146,61,292,49,157,154,62,293,50,158,155,60,291,48,156,153,288,64,52,160,150,289,65,53,161,151,290,63,51,159,152,687,690,691,688,409,488,172,189,440,410,486,173,190,438,408,487,171,191,439,491,412,168,188,443,489,413,169,186,441,490,411,170,187,442,494,415,180,178,446,492,416,181,179,444,493,414,182,177,445,418,497,183,174,449,419,495,184,175,447,417,496,185,176,448,672,665,670,667,374,602,300,83,536,372,600,301,81,534,373,601,302,82,535,605,377,303,79,539,603,375,304,80,537,604,376,305,78,538,608,380,74,306,542,606,378,72,307,540,607,379,73,308,541,383,611,77,309,545,381,609,75,310,543,382,610,76,311,544,673,679,675,682,321,398,130,44,230,322,396,131,42,228,323,397,129,43,229,401,320,126,47,233,399,318,127,45,231,400,319,128,46,232,404,312,39,121,236,402,313,40,122,234,403,314,41,120,235,315,407,38,124,239,316,405,36,125,237,317,406,37,123,238,671,668,669,664,119,500,548,3,476,117,498,546,4,474,118,499,547,5,475,503,115,551,2,479,501,116,549,1,477,502,114,550,0,478,506,110,9,554,482,504,108,10,552,480,505,109,11,553,481,113,509,8,557,485,111,507,6,555,483,112,508,7,556,484,698,695,693,696,572,436,15,420,32,570,437,16,421,30,571,435,17,422,31,432,575,14,423,35,433,573,12,424,33,434,574,13,425,34,644,647,426,646,645,639,638,427,637,636,640,643,428,642,641,659,656,429,658,657,651,649,430,650,648,655,653,431,654,652,701,702,704,703,274,253,243,23,578,275,254,244,21,576,273,252,245,22,577,256,270,242,19,581,257,271,240,20,579,255,272,241,18,580,259,265,29,249,584,260,266,27,250,582,258,264,28,251,583,268,262,25,248,587,269,263,26,246,585,267,261,24,247,586,694,699,700,697,97,215,326,132,464,98,213,324,133,462,96,214,325,134,463,211,100,329,135,467,212,101,327,136,465,210,99,328,137,466,206,103,138,332,470,204,104,139,330,468,205,102,140,331,469,106,209,141,335,473,107,207,142,333,471,105,208,143,334,472,677,676,680,684,524,362,590,278,626,522,360,588,276,624,523,361,589,277,625,365,527,593,281,629,363,525,591,279,627,364,526,592,280,628,368,530,284,596,632,366,528,282,594,630,367,529,283,595,631,533,371,287,599,635,531,369,285,597,633,532,370,286,598,634,681,683,678,674,512,201,614,88,560,510,202,612,89,558,511,203,613,87,559,200,515,617,84,563,198,513,615,85,561,199,514,616,86,562,192,518,94,620,566,193,516,95,618,564,194,517,93,619,565,521,195,90,623,569,519,196,91,621,567,520,197,92,622,568,692,689,686,685 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#58758ff0293182d6dd53be73984d3e209a66569482d3b8502bf477ddaee58f10, 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 17:32:26 · history