Equation 677 Database

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Magma 7ff3a70916fc…

magma 7ff3a70916fc
Size
720
Isomorphism class hash
7ff3a70916fce94b8854cca452b4c18565dc6565d0dbb0ee4151f191a8767300
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 23:56:02
Display reorder
86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,719,69,48,81,70,49,82,56,50,83,57,51,84,58,52,85,59,53,71,60,54,72,61,55,73,62,41,74,63,42,75,64,43,76,65,44,77,66,45,78,67,46,79,68,47,80,31,38,39,40,26,27,28,29,30,33,34,35,36,37,32,716,718,717,715,674,672,671,673,475,461,659,476,462,660,477,463,661,8,464,662,9,465,663,10,466,664,7,467,665,4,468,666,5,469,667,6,470,668,3,471,669,1,472,670,0,473,658,2,474,20,12,13,14,15,16,17,18,19,22,23,24,25,11,21,705,703,704,706,284,330,298,285,331,299,286,332,300,287,333,301,288,334,302,289,335,303,290,336,304,291,337,305,292,338,306,293,339,307,294,340,308,295,326,309,281,327,310,282,328,296,283,329,297,313,320,321,322,323,324,325,311,312,315,316,317,318,319,314,688,690,689,687,197,190,209,198,176,210,199,177,211,200,178,212,201,179,213,202,180,214,203,181,215,204,182,216,205,183,217,191,184,218,192,185,219,193,186,220,194,187,206,195,188,207,196,189,208,171,163,164,165,166,167,168,169,170,173,174,175,161,162,172,695,697,698,696,403,449,416,404,450,417,405,451,418,406,452,419,407,453,420,408,454,421,409,455,422,410,456,423,411,457,424,412,458,425,413,459,426,414,460,427,415,446,428,401,447,429,402,448,430,431,438,439,440,441,442,443,444,445,433,434,435,436,437,432,709,710,707,708,118,111,131,119,112,132,120,113,133,121,114,134,122,115,135,123,101,136,124,102,137,125,103,138,126,104,139,127,105,140,128,106,141,129,107,142,130,108,143,116,109,144,117,110,145,147,154,155,156,157,158,159,160,146,149,150,151,152,153,148,713,712,711,714,649,628,610,650,629,611,651,630,612,652,631,598,653,632,599,654,633,600,655,634,601,656,635,602,657,636,603,643,637,604,644,638,605,645,639,606,646,640,607,647,641,608,648,642,609,626,618,619,620,621,622,623,624,625,613,614,615,616,617,627,702,701,700,699,393,372,354,394,373,355,395,374,341,396,375,342,397,376,343,398,377,344,399,378,345,400,379,346,386,380,347,387,381,348,388,382,349,389,383,350,390,384,351,391,385,352,392,371,353,369,361,362,363,364,365,366,367,368,356,357,358,359,360,370,675,677,678,676,230,273,242,231,274,243,232,275,244,233,276,245,234,277,246,235,278,247,221,279,248,222,280,249,223,266,250,224,267,236,225,268,237,226,269,238,227,270,239,228,271,240,229,272,241,256,263,264,265,251,252,253,254,255,258,259,260,261,262,257,691,693,692,694,517,494,530,518,495,531,519,496,532,520,497,533,521,498,534,522,499,535,508,500,536,509,501,537,510,502,523,511,503,524,512,504,525,513,505,526,514,506,527,515,507,528,516,493,529,490,482,483,484,485,486,487,488,489,492,478,479,480,481,491,682,679,680,681,585,577,545,586,578,546,587,579,547,588,580,548,589,581,549,590,582,550,591,568,551,592,569,552,593,570,538,594,571,539,595,572,540,596,573,541,597,574,542,583,575,543,584,576,544,559,566,567,553,554,555,556,557,558,561,562,563,564,565,560,684,683,686,685 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#7638a5f4265b8c038acb6c1c40b431ab2d5856fd12b04f7ad747e562d533a407, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 57, 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 2026-10-08 23:56:03 · history