Equation 677 Database

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Magma 3cc3da38bc22…

magma 3cc3da38bc22
Size
720
Isomorphism class hash
3cc3da38bc2207c787c13c58c5af53f7ea441660b4f8a41c90483f355d999752
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 01:53:39
Display reorder
596,597,583,584,585,586,587,588,589,590,591,592,593,594,595,719,635,610,621,636,611,622,637,612,623,638,598,624,639,599,625,640,600,626,641,601,627,642,602,613,628,603,614,629,604,615,630,605,616,631,606,617,632,607,618,633,608,619,634,609,620,643,650,651,652,653,654,655,656,657,645,646,647,648,649,644,717,716,718,715,674,672,671,673,134,122,659,135,123,660,136,124,661,137,125,662,138,126,663,139,127,664,140,128,665,141,129,666,142,130,667,143,131,668,144,132,669,145,133,670,146,121,658,147,120,214,221,222,208,209,210,211,212,213,216,217,218,219,220,215,703,704,706,705,389,362,374,390,363,375,391,364,376,392,365,377,393,366,378,394,367,379,395,368,380,396,369,381,397,370,382,398,371,383,399,372,384,400,358,385,401,359,386,402,360,387,388,361,373,345,352,353,354,355,356,357,343,344,347,348,349,350,351,346,690,689,687,688,512,487,498,513,488,499,514,489,500,515,490,501,516,491,502,517,492,503,518,478,504,519,479,505,520,480,506,521,481,507,522,482,493,508,483,494,509,484,495,510,485,496,511,486,497,469,476,477,463,464,465,466,467,468,471,472,473,474,475,470,697,696,698,695,267,226,252,253,227,238,254,228,239,255,229,240,256,230,241,257,231,242,258,232,243,259,233,244,260,234,245,261,235,246,262,236,247,263,237,248,264,223,249,265,224,250,266,225,251,275,282,268,269,270,271,272,273,274,277,278,279,280,281,276,709,708,710,707,545,569,529,546,570,530,547,571,531,548,572,532,549,573,533,550,574,534,551,575,535,552,576,536,538,577,537,539,578,523,540,579,524,541,580,525,542,581,526,543,582,527,544,568,528,567,559,560,561,562,563,564,565,566,554,555,556,557,558,553,713,714,712,711,91,64,76,92,65,77,93,66,78,94,67,79,95,68,80,96,69,81,97,70,82,98,71,83,99,72,84,100,73,85,101,74,86,102,60,87,103,61,88,104,62,89,90,63,75,113,105,106,107,108,109,110,111,112,115,116,117,118,119,114,700,702,701,699,314,287,299,315,288,300,316,289,301,317,290,302,318,291,303,319,292,304,320,293,305,321,294,306,322,295,307,323,296,308,324,297,309,325,283,310,326,284,311,327,285,312,313,286,298,336,328,329,330,331,332,333,334,335,338,339,340,341,342,337,678,675,677,676,437,410,422,438,411,423,439,412,424,440,413,425,441,414,426,442,415,427,443,416,428,444,417,429,445,403,430,446,404,431,447,405,432,433,406,418,434,407,419,435,408,420,436,409,421,461,453,454,455,456,457,458,459,460,448,449,450,451,452,462,692,693,691,694,177,204,162,163,205,148,164,206,149,165,207,150,166,193,151,167,194,152,168,195,153,169,196,154,170,197,155,171,198,156,172,199,157,173,200,158,174,201,159,175,202,160,176,203,161,186,178,179,180,181,182,183,184,185,188,189,190,191,192,187,680,682,679,681,19,58,5,20,59,6,21,45,7,22,46,8,23,47,9,24,48,10,25,49,11,26,50,12,27,51,13,28,52,14,29,53,1,15,54,0,16,55,2,17,56,3,18,57,4,41,33,34,35,36,37,38,39,40,43,44,30,31,32,42,686,684,683,685 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#7c9587bb487c7f78877b32bd3c6516b6b04394ef6d405ed5492c6ed5480f025c, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 45, 49, 53, 57, 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 2026-10-08 01:53:40 · history