Equation 677 Database

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Magma b529a89d161d…

magma b529a89d161d
Size
720
Isomorphism class hash
b529a89d161db41bb6cfeff4acfb1ecb438cc3a5dc2a49ba93eb4d5cdbb662ad
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 14:03:33
Display reorder
18,19,20,21,22,23,24,25,26,27,28,29,15,16,17,719,142,181,178,143,182,179,144,183,165,145,184,166,146,185,167,147,186,168,148,187,169,149,188,170,135,189,171,136,190,172,137,191,173,138,192,174,139,193,175,140,194,176,177,141,180,159,151,152,153,154,155,156,157,158,161,162,163,164,150,160,698,696,695,697,0,344,325,2,330,326,3,331,327,4,332,328,5,333,329,6,334,315,7,335,316,8,336,317,9,337,318,10,338,319,11,339,320,12,340,321,13,341,322,14,342,323,324,1,343,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,718,715,717,716,134,117,98,120,118,99,121,119,100,122,105,101,123,106,102,124,107,103,125,108,104,126,109,90,127,110,91,128,111,92,129,112,93,130,113,94,131,114,95,132,115,96,97,133,116,79,86,87,88,89,75,76,77,78,81,82,83,84,85,80,683,685,684,686,379,361,359,380,362,345,381,363,346,382,364,347,383,365,348,384,366,349,385,367,350,386,368,351,387,369,352,388,370,353,389,371,354,375,372,355,376,373,356,377,374,357,358,378,360,396,403,404,390,391,392,393,394,395,398,399,400,401,402,397,693,691,694,692,429,411,451,430,412,452,431,413,453,432,414,454,433,415,455,434,416,456,420,417,457,421,418,458,422,419,459,423,405,460,424,406,461,425,407,462,426,408,463,427,409,464,450,428,410,448,440,441,442,443,444,445,446,447,435,436,437,438,439,449,705,703,706,704,565,548,529,566,549,530,567,550,531,568,551,532,569,552,533,555,553,534,556,554,535,557,540,536,558,541,537,559,542,538,560,543,539,561,544,525,562,545,526,563,546,527,528,564,547,582,574,575,576,577,578,579,580,581,584,570,571,572,573,583,709,708,710,707,654,71,53,655,72,54,656,73,55,657,74,56,658,60,57,659,61,58,645,62,59,646,63,45,647,64,46,648,65,47,649,66,48,650,67,49,651,68,50,652,69,51,52,653,70,36,43,44,30,31,32,33,34,35,38,39,40,41,42,37,677,678,676,675,243,226,223,244,227,224,245,228,210,246,229,211,247,230,212,248,231,213,249,232,214,250,233,215,251,234,216,252,235,217,253,236,218,254,237,219,240,238,220,241,239,221,222,242,225,204,196,197,198,199,200,201,202,203,206,207,208,209,195,205,699,702,700,701,594,636,617,595,637,618,596,638,619,597,639,620,598,640,621,599,641,622,585,642,623,586,643,624,587,644,625,588,630,626,589,631,627,590,632,628,591,633,629,592,634,615,616,593,635,613,605,606,607,608,609,610,611,612,600,601,602,603,604,614,712,714,711,713,474,515,497,475,516,498,476,517,499,477,518,500,478,519,501,479,520,502,465,521,503,466,522,504,467,523,505,468,524,506,469,510,507,470,511,508,471,512,509,472,513,495,496,473,514,493,485,486,487,488,489,490,491,492,480,481,482,483,484,494,680,682,679,681,294,277,260,295,278,261,296,279,262,297,280,263,298,281,264,299,282,265,285,283,266,286,284,267,287,270,268,288,271,269,289,272,255,290,273,256,291,274,257,292,275,258,259,293,276,313,305,306,307,308,309,310,311,312,300,301,302,303,304,314,687,688,690,689 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#5ea0801c37b7140a4d0f8cc6cd6f875b6a59b1b3f8cb66e6f780ccb36bd56c74, M = {0, 4, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 52, 58, 75} 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 14:03:34 · history