Equation 677 Database

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Magma 4634825d1721…

magma 4634825d1721
Size
720
Isomorphism class hash
4634825d172183f08990aeb92ccd6ababbd918cffebac19c5fd693931619b908
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 02:20:56
Display reorder
88,89,90,91,92,93,94,80,81,82,83,84,85,86,87,719,65,47,63,66,48,64,67,49,50,68,35,51,69,36,52,70,37,53,71,38,54,72,39,55,73,40,56,74,41,57,75,42,58,76,43,59,77,44,60,78,45,61,79,46,62,29,21,22,23,24,25,26,27,28,31,32,33,34,20,30,716,718,717,715,674,672,671,673,469,455,659,470,456,660,471,457,661,472,458,662,473,459,663,474,460,664,475,461,665,476,462,666,477,463,667,4,464,668,2,465,669,1,466,670,3,467,658,0,468,10,17,18,19,5,6,7,8,9,12,13,14,15,16,11,705,703,704,706,328,296,310,329,297,311,330,298,312,331,299,313,332,300,314,333,301,315,334,302,316,320,303,317,321,304,318,322,290,319,323,291,305,324,292,306,325,293,307,326,294,308,327,295,309,279,286,287,288,289,275,276,277,278,281,282,283,284,285,280,688,690,689,687,194,162,176,195,163,177,196,164,178,197,165,179,198,166,180,199,167,181,185,168,182,186,169,183,187,155,184,188,156,170,189,157,171,190,158,172,191,159,173,192,160,174,193,161,175,206,213,214,200,201,202,203,204,205,208,209,210,211,212,207,695,697,698,696,413,443,396,414,444,397,415,445,398,416,446,399,417,447,400,418,448,401,419,449,402,420,450,403,421,451,404,422,452,405,423,453,406,424,454,407,410,440,408,411,441,409,412,442,395,425,432,433,434,435,436,437,438,439,427,428,429,430,431,426,709,710,707,708,98,129,145,99,130,146,100,131,147,101,132,148,102,133,149,103,134,150,104,135,151,105,136,152,106,137,153,107,138,154,108,139,140,109,125,141,95,126,142,96,127,143,97,128,144,110,117,118,119,120,121,122,123,124,112,113,114,115,116,111,713,712,711,714,649,616,632,650,617,633,651,618,634,652,619,635,653,620,636,654,621,637,655,622,638,656,623,639,657,624,640,643,625,641,644,626,642,645,627,628,646,613,629,647,614,630,648,615,631,598,605,606,607,608,609,610,611,612,600,601,602,603,604,599,702,701,700,699,339,371,387,340,372,388,341,373,389,342,374,390,343,375,391,344,376,392,345,377,393,346,378,394,347,379,380,348,365,381,349,366,382,335,367,383,336,368,384,337,369,385,338,370,386,352,359,360,361,362,363,364,350,351,354,355,356,357,358,353,675,677,678,676,238,266,220,239,267,221,240,268,222,241,269,223,242,270,224,243,271,225,244,272,226,230,273,227,231,274,228,232,260,229,233,261,215,234,262,216,235,263,217,236,264,218,237,265,219,249,256,257,258,259,245,246,247,248,251,252,253,254,255,250,691,693,692,694,486,515,530,487,516,531,488,517,532,489,518,533,490,519,534,491,520,535,492,521,536,478,522,537,479,508,523,480,509,524,481,510,525,482,511,526,483,512,527,484,513,528,485,514,529,497,504,505,506,507,493,494,495,496,499,500,501,502,503,498,682,679,680,681,563,593,546,564,594,547,565,595,548,566,596,549,567,597,550,553,583,551,554,584,552,555,585,538,556,586,539,557,587,540,558,588,541,559,589,542,560,590,543,561,591,544,562,592,545,574,581,582,568,569,570,571,572,573,576,577,578,579,580,575,684,683,686,685 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#98b16528073ac7b159dff157031893a3ff21fcc82cd65442bb1543925d4c715a, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 78} 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 02:20:57 · history