Equation 677 Database

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Magma ae5cc4724f88…

magma ae5cc4724f88
Size
720
Isomorphism class hash
ae5cc4724f88955b3a383a32a86f442c8e5a43902380540c25d596bd7cd5d43b
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 11:13:11
Display reorder
585,586,587,588,589,590,591,592,593,594,595,596,597,583,584,719,631,607,614,632,608,615,633,609,616,634,610,617,635,611,618,636,612,619,637,598,620,638,599,621,639,600,622,640,601,623,641,602,624,642,603,625,628,604,626,629,605,627,630,606,613,643,650,651,652,653,654,655,656,657,645,646,647,648,649,644,717,716,718,715,674,671,672,673,199,213,659,200,214,660,201,215,661,202,216,662,203,217,663,204,218,664,205,219,665,206,220,666,207,221,667,208,222,668,209,123,669,210,120,670,211,121,658,212,122,195,187,188,189,190,191,192,193,194,197,198,184,185,186,196,703,704,706,705,383,344,367,384,345,368,385,346,369,386,347,370,387,348,371,373,349,372,374,350,358,375,351,359,376,352,360,377,353,361,378,354,362,379,355,363,380,356,364,381,357,365,382,343,366,394,401,402,388,389,390,391,392,393,396,397,398,399,400,395,690,689,687,688,484,515,468,485,516,469,486,517,470,487,518,471,488,519,472,489,520,473,490,521,474,491,522,475,492,508,476,478,509,477,479,510,463,480,511,464,481,512,465,482,513,466,483,514,467,497,504,505,506,507,493,494,495,496,499,500,501,502,503,498,697,696,698,695,279,242,263,280,243,264,281,244,265,282,245,266,268,246,267,269,247,253,270,248,254,271,249,255,272,250,256,273,251,257,274,252,258,275,238,259,276,239,260,277,240,261,278,241,262,224,231,232,233,234,235,236,237,223,226,227,228,229,230,225,709,708,710,707,541,571,524,542,572,525,543,573,526,544,574,527,545,575,528,546,576,529,547,577,530,548,578,531,549,579,532,550,580,533,551,581,534,552,582,535,538,568,536,539,569,537,540,570,523,553,560,561,562,563,564,565,566,567,555,556,557,558,559,554,713,714,712,711,102,66,87,103,67,88,104,68,89,90,69,75,91,70,76,92,71,77,93,72,78,94,73,79,95,74,80,96,60,81,97,61,82,98,62,83,99,63,84,100,64,85,101,65,86,113,105,106,107,108,109,110,111,112,115,116,117,118,119,114,700,702,701,699,334,311,317,335,312,318,336,298,319,337,299,320,338,300,321,339,301,322,340,302,323,341,303,324,342,304,325,328,305,326,329,306,327,330,307,313,331,308,314,332,309,315,333,310,316,293,285,286,287,288,289,290,291,292,295,296,297,283,284,294,678,675,677,676,453,430,436,454,431,437,455,432,438,456,418,439,457,419,440,458,420,441,459,421,442,460,422,443,461,423,444,462,424,445,448,425,446,449,426,447,450,427,433,451,428,434,452,429,435,413,405,406,407,408,409,410,411,412,415,416,417,403,404,414,692,693,691,694,131,159,181,132,160,182,133,161,183,134,162,169,135,163,170,136,164,171,137,165,172,138,166,173,124,167,174,125,168,175,126,154,176,127,155,177,128,156,178,129,157,179,130,158,180,142,149,150,151,152,153,139,140,141,144,145,146,147,148,143,680,682,679,681,50,29,35,51,15,36,52,16,37,53,17,38,54,18,39,55,19,40,56,20,41,57,21,42,58,22,43,59,23,44,45,24,30,46,25,31,47,26,32,48,27,33,49,28,34,12,4,5,6,7,8,9,10,11,14,1,0,2,3,13,686,684,683,685 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#5e76c6d3b965544f3246a1396d58a622a92ac5abe1044f6db52aefba39d6a87c, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 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 2026-10-07 11:13:17 · history