Equation 677 Database

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Magma a988a7a35e28…

magma a988a7a35e28
Size
720
Isomorphism class hash
a988a7a35e28743e5cf6735eda38b70915377fef30172338ab50d16cfdd13030
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
2026-10-08 21:00:00
Display reorder
70,71,72,73,74,60,61,62,63,64,65,66,67,68,69,719,34,52,15,35,53,16,36,54,17,37,55,18,38,56,19,39,57,20,40,58,21,41,59,22,42,45,23,43,46,24,44,47,25,30,48,26,31,49,27,32,50,28,33,51,29,13,5,6,7,8,9,10,11,12,1,0,2,3,4,14,718,716,717,715,674,672,671,673,474,460,659,475,461,660,476,462,661,477,463,662,442,464,663,443,465,664,444,466,665,441,467,666,438,468,667,439,469,668,440,470,669,437,471,670,436,472,658,435,473,456,448,449,450,451,452,453,454,455,458,459,445,446,447,457,703,705,704,706,273,291,269,274,292,255,275,293,256,276,294,257,277,295,258,278,296,259,279,297,260,280,298,261,281,299,262,282,285,263,283,286,264,284,287,265,270,288,266,271,289,267,272,290,268,310,302,303,304,305,306,307,308,309,312,313,314,300,301,311,690,688,689,687,192,136,174,193,137,175,194,138,176,180,139,177,181,140,178,182,141,179,183,142,165,184,143,166,185,144,167,186,145,168,187,146,169,188,147,170,189,148,171,190,149,172,191,135,173,156,163,164,150,151,152,153,154,155,158,159,160,161,162,157,697,695,698,696,420,377,415,421,378,416,422,379,417,423,380,418,424,381,419,425,382,405,426,383,406,427,384,407,428,385,408,429,386,409,430,387,410,431,388,411,432,389,412,433,375,413,434,376,414,398,390,391,392,393,394,395,396,397,400,401,402,403,404,399,710,709,707,708,93,111,88,94,112,89,95,113,75,96,114,76,97,115,77,98,116,78,99,117,79,100,118,80,101,119,81,102,105,82,103,106,83,104,107,84,90,108,85,91,109,86,92,110,87,130,122,123,124,125,126,127,128,129,132,133,134,120,121,131,712,713,711,714,612,616,654,598,617,655,599,618,656,600,619,657,601,620,643,602,621,644,603,622,645,604,623,646,605,624,647,606,625,648,607,626,649,608,627,650,609,613,651,610,614,652,611,615,653,635,642,628,629,630,631,632,633,634,637,638,639,640,641,636,701,702,700,699,327,331,368,328,332,369,329,333,370,315,334,371,316,335,372,317,336,373,318,337,374,319,338,360,320,339,361,321,340,362,322,341,363,323,342,364,324,343,365,325,344,366,326,330,367,351,358,359,345,346,347,348,349,350,353,354,355,356,357,352,677,675,678,676,199,217,241,200,218,242,201,219,243,202,220,244,203,221,245,204,222,246,205,223,247,206,224,248,207,210,249,208,211,250,209,212,251,195,213,252,196,214,253,197,215,254,198,216,240,237,229,230,231,232,233,234,235,236,239,225,226,227,228,238,693,691,692,694,489,493,530,490,494,531,491,495,532,492,496,533,478,497,534,479,498,535,480,499,536,481,500,537,482,501,523,483,502,524,484,503,525,485,504,526,486,505,527,487,506,528,488,507,529,512,519,520,521,522,508,509,510,511,514,515,516,517,518,513,679,682,680,681,565,570,546,566,571,547,567,572,548,553,573,549,554,574,550,555,575,551,556,576,552,557,577,538,558,578,539,559,579,540,560,580,541,561,581,542,562,582,543,563,568,544,564,569,545,591,583,584,585,586,587,588,589,590,593,594,595,596,597,592,683,684,686,685 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#aa78455ebb848599b7eed3f4eaf5b78527cf031421ada84aeadde26b952ffb1a, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 77} 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 2026-10-08 21:00:01 · history