Equation 677 Database

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Magma 8f161cb8ce13…

magma 8f161cb8ce13
Size
705
Isomorphism class hash
8f161cb8ce13c13561bb508b072fd73c59f36869d22bae5247865bf1a05c1d8e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:29:24
Display reorder
660,529,35,520,538,522,489,33,481,498,482,34,500,518,509,502,31,453,448,455,450,32,469,461,475,462,30,429,421,435,422,649,641,658,26,642,609,601,618,24,602,629,621,638,25,622,569,560,578,29,562,589,580,598,27,582,549,540,558,28,542,685,691,701,699,527,96,534,528,531,487,97,494,488,491,98,514,508,507,511,99,442,445,443,444,100,467,472,468,470,101,427,432,428,430,647,654,648,102,651,607,614,608,103,611,627,634,628,104,631,567,574,568,105,571,587,594,588,106,591,547,554,548,107,551,692,688,703,686,95,137,257,115,78,93,135,255,116,79,136,256,114,94,80,133,91,253,118,81,134,92,254,119,82,132,90,252,117,83,86,263,113,143,76,84,261,111,141,77,85,262,112,142,75,89,259,109,139,72,87,260,110,140,73,88,258,108,138,74,663,674,666,682,317,232,377,389,365,315,233,375,387,363,231,376,388,316,364,228,313,373,385,361,229,314,374,386,362,230,312,372,384,360,323,383,395,238,371,321,381,393,239,369,322,382,394,237,370,319,379,391,234,367,320,380,392,235,368,318,378,390,236,366,677,676,670,680,526,9,521,533,525,486,10,480,493,485,11,501,513,506,505,8,452,449,454,451,6,466,460,471,465,7,426,420,431,425,646,640,653,1,645,606,600,613,0,605,626,620,633,2,625,566,561,573,3,565,586,581,593,4,585,546,541,553,5,545,700,695,698,694,532,12,530,536,539,492,13,490,496,499,14,510,516,512,519,15,456,457,458,459,16,476,477,478,479,17,436,437,438,439,652,650,656,18,659,612,610,616,19,619,632,630,636,20,639,572,570,576,21,579,592,590,596,22,599,552,550,556,23,559,687,696,689,693,523,190,524,535,537,483,191,484,495,497,189,504,515,503,517,186,440,441,446,447,187,463,464,473,474,188,423,424,433,434,643,644,655,181,657,603,604,615,182,617,623,624,635,180,637,563,564,575,184,577,583,584,595,185,597,543,544,555,183,557,704,697,702,690,68,222,353,401,212,66,223,351,399,210,224,352,400,67,211,225,71,349,397,215,226,69,350,398,213,227,70,348,396,214,63,359,407,220,207,64,357,405,221,208,65,358,406,219,209,62,355,403,216,206,60,356,404,217,204,61,354,402,218,205,675,679,678,683,329,125,293,413,151,327,123,291,411,152,124,292,412,328,150,121,325,289,409,154,122,326,290,410,155,120,324,288,408,153,335,299,419,131,149,333,297,417,129,147,334,298,418,130,148,331,295,415,127,145,332,296,416,128,146,330,294,414,126,144,668,681,672,684,305,194,269,341,245,303,192,267,339,243,193,268,340,304,244,197,301,265,337,241,195,302,266,338,242,196,300,264,336,240,311,275,347,200,251,309,273,345,198,249,310,274,346,199,250,307,271,343,203,247,308,272,344,201,248,306,270,342,202,246,665,661,669,673,162,40,51,179,281,163,41,52,177,279,39,53,178,164,280,36,165,50,175,277,37,166,48,176,278,38,167,49,174,276,160,57,170,46,287,161,58,168,47,285,159,59,169,45,286,156,56,173,42,283,157,54,171,43,284,158,55,172,44,282,671,667,662,664 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 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#1c6b3e96bd585e9e8fd52e93592fcd11cb6c83a04227bfcba3bf653b0809cf1c, M = {60} 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 2026-10-03 15:29:25 · history