Equation 677 Database

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Magma e86a62777964…

magma e86a62777964
Size
720
Isomorphism class hash
e86a62777964b877068a26f2333cce23f8596280c00f32414d13abf500d08208
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 23:50:13
Display reorder
38,39,40,41,42,43,44,30,31,32,33,34,35,36,37,719,452,478,441,442,453,479,443,454,465,444,455,466,445,456,467,446,457,468,447,458,469,448,459,470,449,460,471,435,461,472,436,462,473,437,463,474,438,464,475,450,439,476,451,440,477,494,486,487,488,489,490,491,492,493,481,482,483,484,485,480,695,697,698,696,47,72,624,625,48,73,626,49,74,627,50,60,628,51,61,629,52,62,615,53,63,616,54,64,617,55,65,618,56,66,619,57,67,620,58,68,621,59,69,45,622,70,46,623,71,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,715,718,716,717,409,434,399,400,410,420,401,411,421,402,412,422,403,413,423,404,414,424,390,415,425,391,416,426,392,417,427,393,418,428,394,419,429,395,405,430,396,406,431,407,397,432,408,398,433,381,388,389,375,376,377,378,379,380,383,384,385,386,387,382,684,685,683,686,82,91,125,126,83,92,127,84,93,128,85,94,129,86,95,130,87,96,131,88,97,132,89,98,133,75,99,134,76,100,120,77,101,121,78,102,122,79,103,80,123,104,81,124,90,108,115,116,117,118,119,105,106,107,110,111,112,113,114,109,694,692,691,693,162,171,137,138,163,172,139,164,173,140,150,174,141,151,175,142,152,176,143,153,177,144,154,178,145,155,179,146,156,165,147,157,166,148,158,167,149,159,168,160,135,169,161,136,170,188,180,181,182,183,184,185,186,187,190,191,192,193,194,189,703,705,704,706,287,313,276,277,288,314,278,289,300,279,290,301,280,291,302,281,292,303,282,293,304,283,294,305,284,295,306,270,296,307,271,297,308,272,298,309,273,299,310,285,274,311,286,275,312,258,265,266,267,268,269,255,256,257,260,261,262,263,264,259,710,708,709,707,639,650,29,15,640,651,16,641,652,17,642,653,18,643,654,19,644,655,20,630,656,21,631,657,22,632,658,23,633,659,24,634,645,25,635,646,26,636,647,637,27,648,638,28,649,10,2,3,4,5,6,7,8,9,12,13,14,1,0,11,676,678,677,675,544,499,534,535,545,500,536,546,501,537,547,502,538,548,503,539,549,504,525,550,505,526,551,506,527,552,507,528,553,508,529,554,509,530,540,495,531,541,496,542,532,497,543,533,498,516,523,524,510,511,512,513,514,515,518,519,520,521,522,517,700,702,699,701,316,340,360,361,317,341,362,318,342,363,319,343,364,320,344,365,321,330,366,322,331,367,323,332,368,324,333,369,325,334,370,326,335,371,327,336,372,328,337,329,373,338,315,374,339,356,348,349,350,351,352,353,354,355,358,359,345,346,347,357,711,714,712,713,245,200,235,236,246,201,237,247,202,238,248,203,239,249,204,225,250,205,226,251,206,227,252,207,228,253,208,229,254,209,230,240,195,231,241,196,232,242,197,243,233,198,244,234,199,216,223,224,210,211,212,213,214,215,218,219,220,221,222,217,682,680,681,679,594,604,570,571,595,605,572,596,606,573,597,607,574,598,608,575,599,609,576,585,610,577,586,611,578,587,612,579,588,613,580,589,614,581,590,600,582,591,601,592,583,602,593,584,603,566,558,559,560,561,562,563,564,565,568,569,555,556,557,567,687,688,690,689 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#9ec34e5d7233e8953a2fa801c206b195473c59d0c7836b1f0f582edb83284699, M = {0, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 44, 48, 54, 58, 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 23:50:14 · history