Equation 677 Database

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Magma 8c8a33728e4b…

magma 8c8a33728e4b
Size
705
Isomorphism class hash
8c8a33728e4bdae49ec9deebb49ed2c9b1f9690c7b37e28b90c7a19c4b84916e
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 16:33:12
Display reorder
660,512,516,110,506,507,108,532,526,527,536,109,496,492,486,487,113,432,436,427,420,111,450,453,448,449,112,472,476,466,467,636,626,632,116,627,656,646,652,114,647,616,606,612,115,607,546,558,554,119,547,566,578,574,117,567,118,586,598,594,587,688,699,692,687,503,510,63,509,504,64,523,529,524,530,65,490,483,489,484,62,424,430,429,425,60,455,458,457,445,61,463,470,469,464,630,629,623,69,624,650,649,643,70,644,610,609,603,71,604,549,552,543,68,544,569,572,563,66,564,67,589,592,583,584,686,701,690,693,388,328,51,210,304,52,389,211,305,329,53,327,387,212,303,50,384,324,213,300,48,385,325,214,301,49,386,326,215,302,334,208,394,57,310,335,209,395,58,311,333,207,393,59,309,204,330,390,56,306,205,331,391,54,307,55,206,332,392,308,663,680,675,668,292,276,183,133,261,184,293,134,262,277,185,278,291,132,263,182,288,279,136,260,180,289,280,137,258,181,290,281,135,259,282,139,298,189,252,283,140,299,190,253,284,138,297,191,254,142,285,294,188,255,143,286,295,186,256,187,141,287,296,257,665,661,677,666,514,501,9,502,505,10,534,522,525,521,11,480,494,482,485,8,434,421,423,426,6,447,443,444,446,7,474,460,462,465,620,622,634,1,625,641,642,654,0,645,600,602,614,2,605,542,540,556,3,545,562,561,576,4,565,5,582,581,596,585,703,698,700,696,518,519,275,517,513,273,538,537,533,539,274,499,498,497,493,271,438,439,437,433,272,441,442,440,451,270,477,479,478,473,639,638,637,266,633,657,658,659,264,653,619,618,617,265,613,550,559,551,269,555,570,579,571,267,575,268,590,599,591,595,697,691,704,685,511,500,105,508,515,106,531,528,535,520,107,481,491,488,495,104,431,422,428,435,102,459,454,456,452,103,471,461,468,475,621,628,631,96,635,640,648,651,97,655,601,608,611,98,615,548,541,553,99,557,568,560,573,100,577,101,588,580,593,597,702,694,689,695,33,169,147,165,404,148,34,166,406,170,149,168,35,167,402,146,32,172,164,397,144,30,173,162,398,145,31,171,163,400,175,156,24,153,417,176,157,25,154,419,174,158,26,155,415,159,178,27,152,409,160,179,28,150,411,151,161,177,29,413,681,683,671,678,246,352,39,15,364,40,247,16,365,353,41,351,248,17,363,38,249,348,14,360,36,250,349,12,361,37,251,350,13,362,358,21,244,45,370,359,22,245,46,371,357,23,243,47,369,20,354,240,44,366,18,355,241,42,367,43,19,356,242,368,676,670,684,673,131,316,203,376,76,201,129,377,77,317,202,315,130,375,75,199,127,312,372,72,200,128,313,373,73,198,126,314,374,74,322,382,122,194,82,323,383,120,192,83,321,381,121,193,81,378,318,125,197,78,379,319,123,195,79,196,380,320,124,80,674,667,679,664,340,405,94,232,222,95,341,233,223,407,93,403,339,231,224,90,336,396,228,225,91,337,399,229,226,92,338,401,230,227,416,238,346,85,220,418,239,347,86,221,414,237,345,84,219,234,408,342,88,216,235,410,343,89,217,87,236,412,344,218,669,672,662,682 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#3519a427d5ae28e51e8dce355af6af1aa210384ac7088475411fc50e96b55163, 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 16:33:13 · history