Equation 677 Database

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Magma 6412c10f66c6…

magma 6412c10f66c6
Size
705
Isomorphism class hash
6412c10f66c6ffbbc720838a63e21b20f15d0b9491476bae61139868df7752a6
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 18:19:20
Display reorder
660,532,38,521,537,520,492,36,480,497,481,517,37,512,501,500,453,41,447,454,448,471,39,461,474,460,431,40,420,434,421,44,640,652,657,641,42,601,612,617,600,43,620,632,637,621,561,47,572,577,560,581,45,592,597,580,541,46,552,557,540,686,701,688,685,538,95,523,533,535,498,93,483,493,495,513,94,518,503,515,455,91,440,445,446,475,92,462,472,473,435,90,422,432,433,86,643,658,653,655,84,603,618,613,615,85,623,638,633,635,563,89,578,573,575,583,87,598,593,595,543,88,558,553,555,697,692,695,690,108,247,68,16,295,109,248,66,17,296,15,246,110,67,294,111,250,71,12,298,112,251,69,13,299,113,249,70,14,297,245,63,114,22,293,243,64,115,23,291,244,65,116,21,292,62,241,117,18,289,60,242,118,19,290,61,240,119,20,288,671,678,662,674,221,8,341,281,266,219,6,339,279,264,280,7,220,340,265,217,11,337,277,269,218,9,338,278,267,216,10,336,276,268,3,347,227,287,272,4,345,225,285,270,5,346,226,286,271,343,2,223,283,275,344,1,224,284,273,342,0,222,282,274,682,661,668,665,536,120,525,528,524,496,121,485,488,484,508,122,516,505,504,456,123,450,451,449,478,124,464,467,463,436,125,424,427,423,126,645,656,648,644,127,605,616,608,604,128,625,636,628,624,565,129,576,568,564,585,130,596,588,584,545,131,556,548,544,703,687,699,702,531,207,522,534,539,491,208,482,494,499,514,209,511,502,519,452,206,457,458,459,470,204,476,477,479,430,205,437,438,439,213,642,651,654,659,214,602,611,614,619,215,622,631,634,639,562,212,571,574,579,582,210,591,594,599,542,211,551,554,559,700,693,691,698,527,31,529,530,526,487,32,489,490,486,510,30,507,509,506,442,34,443,444,441,466,35,468,469,465,426,33,428,429,425,29,649,647,650,646,27,609,607,610,606,28,629,627,630,626,569,25,567,570,566,589,26,587,590,586,549,24,547,550,546,704,689,694,696,99,79,377,143,145,100,80,375,141,146,142,78,101,376,144,98,82,373,139,148,96,83,374,140,149,97,81,372,138,147,77,383,105,134,151,75,381,106,132,152,76,382,107,133,150,379,73,104,137,154,380,74,102,135,155,378,72,103,136,153,666,673,680,675,193,55,413,389,187,194,56,411,387,188,388,54,192,412,186,196,58,409,385,190,197,59,410,386,191,195,57,408,384,189,53,419,199,395,185,51,417,200,393,183,52,418,198,394,184,415,49,202,391,181,416,50,203,392,182,414,48,201,390,180,669,676,681,684,230,255,401,329,305,228,256,399,327,303,328,257,229,400,304,233,254,397,325,301,231,252,398,326,302,232,253,396,324,300,261,407,236,335,311,262,405,234,333,309,263,406,235,334,310,403,260,239,331,307,404,258,237,332,308,402,259,238,330,306,663,664,670,677,365,322,353,165,179,363,323,351,166,177,167,321,364,352,178,361,318,349,164,175,362,319,350,162,176,360,320,348,163,174,313,359,371,156,170,314,357,369,157,168,312,358,370,158,169,355,316,367,159,173,356,317,368,160,171,354,315,366,161,172,679,683,672,667 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#7b2d22e166b1ff02dad840b7a1389a143f850a338adb3bda964b6fc81ff7fb8b, 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 18:19:21 · history