Equation 677 Database

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Magma 76eb7a1be17d…

magma 76eb7a1be17d
Size
720
Isomorphism class hash
76eb7a1be17d9d9ef7fa73463bd7dbbcc3c45bfd050fa326b506ccf9f8c92935
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 15:10:34
Display reorder
11,12,13,14,15,16,17,18,19,20,23,25,27,29,10,719,160,143,120,161,121,144,162,122,145,163,123,146,164,124,147,150,125,148,126,149,151,152,127,135,153,128,136,154,129,137,155,130,138,156,131,139,157,132,140,158,133,141,159,134,142,118,110,111,112,113,114,115,116,117,105,106,107,108,109,119,695,697,698,696,317,301,295,318,296,302,319,297,303,320,298,304,321,299,305,322,285,306,286,307,323,324,287,308,325,288,309,326,289,310,327,290,311,328,291,312,329,292,313,315,293,314,316,294,300,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,715,718,716,717,88,71,49,89,50,72,75,51,73,76,52,74,77,53,60,78,54,61,55,62,79,80,56,63,81,57,64,82,58,65,83,59,66,84,45,67,85,46,68,86,47,69,87,48,70,98,90,91,92,93,94,95,96,97,100,101,102,103,104,99,684,685,683,686,380,364,357,381,358,365,382,359,366,383,345,367,384,346,368,385,347,369,348,370,386,387,349,371,388,350,372,389,351,373,375,352,374,376,353,360,377,354,361,378,355,362,379,356,363,338,330,331,332,333,334,335,336,337,340,341,342,343,344,339,694,691,693,692,432,415,392,433,393,416,434,394,417,420,395,418,421,396,419,422,397,405,398,406,423,424,399,407,425,400,408,426,401,409,427,402,410,428,403,411,429,404,412,430,390,413,431,391,414,443,435,436,437,438,439,440,441,442,445,446,447,448,449,444,703,705,704,706,555,554,533,556,534,540,557,535,541,558,536,542,559,537,543,560,538,544,539,545,561,562,525,546,563,526,547,564,527,548,565,528,549,566,529,550,567,530,551,568,531,552,569,532,553,514,521,522,523,524,510,511,512,513,516,517,518,519,520,515,710,708,709,707,42,650,642,43,643,651,44,644,652,30,630,653,31,631,654,32,632,655,633,656,33,34,634,657,35,635,658,36,636,659,37,637,645,38,638,646,39,639,647,40,640,648,41,641,649,21,3,4,5,6,7,8,9,1,24,26,28,0,2,22,676,678,677,675,181,179,211,182,212,165,183,213,166,184,214,167,185,215,168,186,216,169,217,170,187,188,218,171,189,219,172,190,220,173,191,221,174,192,222,175,193,223,176,194,224,177,180,210,178,208,200,201,202,203,204,205,206,207,195,196,197,198,199,209,700,702,699,701,627,610,589,628,590,611,629,591,612,615,592,613,616,593,614,617,594,600,595,601,618,619,596,602,620,597,603,621,598,604,622,599,605,623,585,606,624,586,607,625,587,608,626,588,609,572,579,580,581,582,583,584,570,571,574,575,576,577,578,573,711,714,712,713,472,456,500,473,501,457,474,502,458,475,503,459,476,504,460,477,505,461,506,462,478,479,507,463,465,508,464,466,509,450,467,495,451,468,496,452,469,497,453,470,498,454,471,499,455,482,489,490,491,492,493,494,480,481,484,485,486,487,488,483,682,680,681,679,250,234,278,251,279,235,252,280,236,253,281,237,254,282,238,240,283,239,284,225,241,242,270,226,243,271,227,244,272,228,245,273,229,246,274,230,247,275,231,248,276,232,249,277,233,260,267,268,269,255,256,257,258,259,262,263,264,265,266,261,687,688,690,689 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#7fd9b57d9d47f149dcae21b99bbb486e9ed16acb343863fc90869d5061310077, M = {0, 4, 8, 12, 16, 20, 26, 28, 32, 36, 40, 44, 48, 52, 57, 77} 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 15:10:35 · history