Equation 677 Database

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Magma 3829a4ad0d9f…

magma 3829a4ad0d9f
Size
720
Isomorphism class hash
3829a4ad0d9f513a08862402bcab12b897458ce0ec0963e5688c59456cc95200
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 10:10:38
Display reorder
71,72,73,74,75,76,77,63,64,65,66,67,68,69,70,719,32,14,36,37,18,15,19,38,16,39,20,17,40,21,3,41,22,4,42,23,5,43,24,6,44,25,7,45,26,8,46,27,9,47,28,10,33,29,11,34,30,12,35,31,13,54,61,62,48,49,50,51,52,53,56,57,58,59,60,55,716,718,715,717,672,671,674,673,467,453,468,659,454,660,469,455,661,470,456,662,471,457,663,472,458,664,473,459,665,474,460,666,475,461,667,476,462,668,477,463,669,1,464,670,0,465,658,2,466,449,441,442,443,444,445,446,447,448,451,452,438,439,440,450,705,703,706,704,285,268,302,288,286,269,287,289,270,290,273,271,291,274,272,292,275,258,293,276,259,294,277,260,295,278,261,296,279,262,297,280,263,298,281,264,299,282,265,300,283,266,301,284,267,304,311,312,313,314,315,316,317,303,306,307,308,309,310,305,688,690,687,689,151,190,153,154,152,191,138,155,192,156,139,193,157,140,194,158,141,195,159,142,196,160,143,197,161,144,183,162,145,184,163,146,185,164,147,186,165,148,187,166,149,188,167,150,189,172,179,180,181,182,168,169,170,171,174,175,176,177,178,173,695,697,696,698,409,407,427,428,410,393,411,429,394,430,412,395,431,413,396,432,414,397,433,415,398,434,416,399,435,417,400,436,418,401,437,419,402,423,420,403,424,421,404,425,422,405,426,408,406,390,382,383,384,385,386,387,388,389,392,378,379,380,381,391,709,710,708,707,122,105,124,125,108,106,109,126,107,127,110,93,128,111,94,129,112,95,130,113,96,131,114,97,132,115,98,133,116,99,134,117,100,135,118,101,136,119,102,137,120,103,123,121,104,88,80,81,82,83,84,85,86,87,90,91,92,78,79,89,713,712,714,711,654,636,601,602,655,637,656,603,638,604,657,639,605,643,640,606,644,641,607,645,642,608,646,628,609,647,629,610,648,630,611,649,631,612,650,632,598,651,633,599,652,634,600,653,635,619,626,627,613,614,615,616,617,618,621,622,623,624,625,620,702,701,699,700,363,361,326,327,364,362,365,328,348,329,366,349,330,367,350,331,368,351,332,369,352,318,370,353,319,371,354,320,372,355,321,373,356,322,374,357,323,375,358,324,376,359,325,377,360,344,336,337,338,339,340,341,342,343,346,347,333,334,335,345,675,677,676,678,199,254,217,218,200,255,201,219,256,220,202,257,221,203,243,222,204,244,223,205,245,224,206,246,225,207,247,226,208,248,227,209,249,213,210,250,214,211,251,215,212,252,216,198,253,236,228,229,230,231,232,233,234,235,238,239,240,241,242,237,691,693,694,692,483,537,502,503,484,523,485,504,524,505,486,525,506,487,526,507,488,527,493,489,528,494,490,529,495,491,530,496,492,531,497,478,532,498,479,533,499,480,534,500,481,535,501,482,536,520,512,513,514,515,516,517,518,519,522,508,509,510,511,521,682,679,681,680,596,579,545,546,597,580,583,547,581,548,584,582,549,585,568,550,586,569,551,587,570,552,588,571,538,589,572,539,590,573,540,591,574,541,592,575,542,593,576,543,594,577,544,595,578,562,554,555,556,557,558,559,560,561,564,565,566,567,553,563,684,683,685,686 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 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#7df1be11e8b03a352a732fe3cebbb8055958b1c7efe44dbc5799cf88069697db, M = {0, 4, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 75} 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 2026-10-07 10:10:39 · history