Equation 677 Database

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Magma ed5745e30cdd…

magma ed5745e30cdd
Size
705
Isomorphism class hash
ed5745e30cdd19a13fc3d28f65b6298ebffcc05f9d443fc4a342118c841520b8
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 16:37:18
Display reorder
660,232,545,230,207,254,233,546,205,231,255,206,547,234,229,253,548,235,203,226,250,549,236,204,227,251,550,237,202,228,252,543,238,221,198,245,544,239,222,196,246,542,240,220,197,244,539,241,224,201,248,540,242,225,199,249,541,243,223,200,247,662,664,670,665,361,338,340,264,319,362,339,262,341,320,263,337,363,342,321,334,360,267,343,318,335,358,265,344,316,336,359,266,345,317,329,352,346,259,325,330,353,347,260,326,328,354,348,261,327,332,355,349,258,324,333,356,350,256,322,331,357,351,257,323,685,690,687,688,189,466,478,143,533,187,467,144,479,534,142,468,188,480,535,469,185,146,481,536,470,186,147,482,537,471,184,145,483,538,464,195,476,141,531,465,193,477,139,532,463,194,475,140,530,460,191,472,137,527,461,192,473,138,528,462,190,474,136,529,671,669,663,666,93,370,276,59,10,94,371,57,274,11,58,372,95,275,12,373,96,62,279,9,374,97,60,277,7,375,98,61,278,8,368,99,271,65,16,369,100,272,63,17,367,101,273,64,18,364,102,270,68,15,365,103,268,66,13,366,104,269,67,14,673,679,674,680,442,509,288,106,521,443,510,107,286,522,105,511,444,287,523,512,445,109,291,524,513,446,110,289,525,514,447,108,290,526,507,440,283,112,519,508,441,284,113,520,506,439,285,111,518,503,436,282,115,515,504,437,280,116,516,505,438,281,114,517,661,668,667,672,418,497,209,183,20,419,498,181,210,21,182,499,420,208,19,500,421,179,212,23,501,422,180,213,24,502,423,178,211,22,495,416,215,174,26,496,417,216,172,27,494,415,214,173,25,491,412,218,177,29,492,413,219,175,30,493,414,217,176,28,694,693,695,696,484,629,50,92,49,642,643,90,641,640,91,647,646,645,644,651,650,88,648,649,655,654,89,653,652,659,658,87,657,656,627,490,56,83,43,628,488,54,81,44,626,489,55,82,45,623,486,52,86,46,624,487,53,84,47,625,485,51,85,48,701,702,704,703,593,117,557,302,1,594,630,303,558,631,301,633,595,559,632,634,596,298,560,635,636,597,299,561,637,638,598,300,562,639,123,591,555,293,2,121,592,556,294,3,122,590,554,292,0,119,587,551,296,5,120,588,552,297,6,118,589,553,295,4,698,699,700,697,581,406,167,40,394,582,407,41,168,395,42,408,583,166,396,409,584,39,170,397,410,585,37,171,398,411,586,38,169,399,404,579,165,31,392,405,580,163,32,393,403,578,164,33,391,400,575,161,34,388,401,576,162,35,389,402,577,160,36,390,682,675,676,684,605,454,129,307,569,606,455,308,127,570,309,456,607,128,571,457,608,306,125,572,458,609,304,126,573,459,610,305,124,574,452,603,135,313,567,453,604,133,314,568,451,602,134,315,566,448,599,131,312,563,449,600,132,310,564,450,601,130,311,565,683,681,677,678,148,617,430,381,72,149,618,379,431,73,380,619,150,432,74,620,151,377,433,71,621,152,378,434,69,622,153,376,435,70,615,154,428,387,78,616,155,429,385,79,614,156,427,386,80,611,157,424,383,77,612,158,425,384,75,613,159,426,382,76,689,691,692,686 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#368900d303714df43b3718b8680935166fd1150994cfe143b7c0fba0a5b985be, 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 16:37:19 · history