Equation 677 Database

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Magma 4453866a3426…

magma 4453866a3426
Size
705
Isomorphism class hash
4453866a342639270749b245bedfa60835e2d9e4f8eb120d65774dbcb6f171bf
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 17:37:58
Display reorder
660,57,516,506,505,514,534,536,58,526,525,496,494,59,486,485,434,56,436,421,426,54,452,453,449,448,474,55,476,466,465,626,634,48,636,625,654,49,656,646,645,614,50,616,606,605,51,556,558,546,545,52,576,578,566,565,53,596,598,586,585,692,687,690,703,268,509,507,500,504,524,529,269,527,520,489,484,267,487,480,425,264,429,427,420,265,455,457,456,443,464,266,469,467,460,627,624,274,629,620,644,275,649,647,641,604,273,609,607,600,270,544,551,549,540,271,564,571,569,561,272,584,591,589,581,685,702,691,698,47,118,124,388,364,365,119,45,125,389,117,363,46,123,387,360,43,114,120,384,44,361,115,121,385,362,42,116,122,386,130,370,38,109,394,371,36,110,131,395,369,37,108,129,393,41,366,112,126,390,39,367,113,127,391,40,368,111,128,392,662,670,668,677,149,26,175,180,201,202,24,147,176,181,25,203,148,174,182,200,145,29,178,183,146,198,27,179,184,199,144,28,177,185,173,192,155,32,186,193,153,30,171,187,194,154,31,172,188,151,195,35,169,189,152,196,33,170,190,150,197,34,168,191,673,671,680,683,95,502,503,515,508,528,522,93,523,535,482,488,94,483,495,428,91,423,424,435,92,446,444,445,447,468,90,462,463,475,623,628,86,622,635,648,84,642,643,655,608,85,602,603,615,89,550,542,543,557,87,570,562,563,577,88,590,582,583,597,688,701,704,695,4,517,518,512,519,539,537,5,538,532,497,499,3,498,492,439,1,437,438,432,0,442,440,441,450,479,2,478,477,472,637,639,10,638,632,657,11,658,659,652,619,9,618,617,612,6,559,547,548,554,7,579,567,568,574,8,599,587,588,594,693,699,697,686,77,501,510,513,511,531,521,75,530,533,481,491,76,490,493,431,73,422,430,433,74,459,454,458,451,471,72,461,470,473,630,631,83,621,633,651,81,640,650,653,611,82,601,610,613,79,553,541,552,555,80,573,560,572,575,78,593,580,592,595,696,689,694,700,21,299,304,352,277,278,297,22,305,353,298,276,23,303,351,280,20,295,300,348,18,281,296,301,349,279,19,294,302,350,310,283,12,290,358,284,13,288,311,359,282,14,289,309,357,15,286,293,306,354,16,287,291,307,355,17,285,292,308,356,661,666,676,681,158,208,328,135,412,413,209,156,329,136,207,411,157,327,137,408,161,204,324,134,159,409,205,325,132,410,160,206,326,133,334,418,164,214,141,419,162,215,335,142,417,163,213,333,143,167,414,210,330,140,165,415,211,331,138,166,416,212,332,139,664,675,684,679,61,376,340,263,400,401,377,62,341,261,375,399,60,339,262,396,64,372,336,259,65,397,373,337,260,398,63,374,338,258,346,406,67,382,254,407,68,383,347,252,405,66,381,345,253,70,402,378,342,257,71,403,379,343,255,69,404,380,344,256,665,682,678,669,251,226,233,104,316,317,227,249,231,102,225,315,250,232,103,312,247,222,229,107,248,313,223,230,105,314,246,224,228,106,239,322,242,217,99,323,240,218,237,100,321,241,216,238,101,245,318,220,235,98,243,319,221,236,96,244,320,219,234,97,674,672,663,667 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#5b838974e03a318bd69da9937fbfbee1bd56d732e0aad8a944a467873e322378, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 17:37:59 · history