Equation 677 Database

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Magma 330baa45e8da…

magma 330baa45e8da
Size
720
Isomorphism class hash
330baa45e8da68cbc508ee17d7734796ca7a89726bfa9fc52d37f301b1f2cd07
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 04:39:33
Display reorder
18,19,20,21,22,23,24,25,26,27,28,29,15,16,17,719,144,194,161,145,180,162,146,181,163,147,182,164,148,183,150,149,184,151,135,185,152,136,186,153,137,187,154,138,188,155,139,189,156,140,190,157,141,191,158,142,192,159,143,193,160,177,169,170,171,172,173,174,175,176,179,165,166,167,168,178,697,695,698,696,344,328,2,330,329,3,331,315,4,332,316,5,333,317,6,334,318,7,335,319,8,336,320,9,337,321,10,338,322,11,339,323,12,340,324,13,341,325,14,342,326,1,343,327,0,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,718,715,716,717,101,83,118,102,84,119,103,85,105,104,86,106,90,87,107,91,88,108,92,89,109,93,75,110,94,76,111,95,77,112,96,78,113,97,79,114,98,80,115,99,81,116,100,82,117,133,125,126,127,128,129,130,131,132,120,121,122,123,124,134,685,684,683,686,357,394,374,358,395,360,359,396,361,345,397,362,346,398,363,347,399,364,348,400,365,349,401,366,350,402,367,351,403,368,352,404,369,353,390,370,354,391,371,355,392,372,356,393,373,376,383,384,385,386,387,388,389,375,378,379,380,381,382,377,693,694,691,692,413,451,431,414,452,432,415,453,433,416,454,434,417,455,420,418,456,421,419,457,422,405,458,423,406,459,424,407,460,425,408,461,426,409,462,427,410,463,428,411,464,429,412,450,430,448,440,441,442,443,444,445,446,447,435,436,437,438,439,449,704,705,706,703,569,553,571,555,554,572,556,540,573,557,541,574,558,542,575,559,543,576,560,544,577,561,545,578,562,546,579,563,547,580,564,548,581,565,549,582,566,550,583,567,551,584,568,552,570,534,526,527,528,529,530,531,532,533,536,537,538,539,525,535,708,710,709,707,655,50,66,656,51,67,657,52,68,658,53,69,659,54,70,645,55,71,646,56,72,647,57,73,648,58,74,649,59,60,650,45,61,651,46,62,652,47,63,653,48,64,654,49,65,33,40,41,42,43,44,30,31,32,35,36,37,38,39,34,678,676,677,675,203,241,221,204,242,222,205,243,223,206,244,224,207,245,210,208,246,211,209,247,212,195,248,213,196,249,214,197,250,215,198,251,216,199,252,217,200,253,218,201,254,219,202,240,220,238,230,231,232,233,234,235,236,237,225,226,227,228,229,239,702,700,699,701,619,603,636,620,604,637,621,605,638,622,606,639,623,607,640,624,608,641,625,609,642,626,610,643,627,611,644,628,612,630,629,613,631,615,614,632,616,600,633,617,601,634,618,602,635,586,593,594,595,596,597,598,599,585,588,589,590,591,592,587,714,711,712,713,510,507,474,511,508,475,512,509,476,513,495,477,514,496,478,515,497,479,516,498,465,517,499,466,518,500,467,519,501,468,520,502,469,521,503,470,522,504,471,523,505,472,524,506,473,490,482,483,484,485,486,487,488,489,492,493,494,480,481,491,681,680,679,682,280,264,296,281,265,297,282,266,298,283,267,299,284,268,285,270,269,286,271,255,287,272,256,288,273,257,289,274,258,290,275,259,291,276,260,292,277,261,293,278,262,294,279,263,295,311,303,304,305,306,307,308,309,310,313,314,300,301,302,312,688,687,690,689 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#82fda0c11d8b67dd90198c9d834359ac6146390672939dae5a097a0c09da5164, M = {0, 4, 8, 12, 16, 20, 24, 28, 33, 37, 41, 45, 49, 53, 57, 78} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 04:39:34 · history