Equation 677 Database

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Magma 3b113c246f6a…

magma 3b113c246f6a
Size
705
Isomorphism class hash
3b113c246f6a94d18621981f8656e6bdd9f87f4b8fcccd8df0c37551d8d31a08
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 18:13:55
Display reorder
660,461,466,205,473,471,428,430,433,206,427,441,446,204,455,451,526,522,208,534,531,486,482,209,494,491,506,502,207,514,511,580,586,211,594,591,541,546,212,554,551,561,566,210,574,571,646,641,214,654,651,606,601,215,614,611,626,621,213,634,631,685,697,693,699,469,467,66,462,468,426,424,420,67,425,449,447,68,440,448,527,529,69,521,528,487,489,70,480,488,507,509,71,501,508,589,587,64,581,588,549,547,65,540,548,569,567,63,560,568,647,649,60,640,648,607,609,61,600,608,627,629,62,620,628,687,686,688,696,177,314,46,154,338,178,312,155,47,336,179,313,45,153,337,317,176,42,150,341,315,174,43,151,339,316,175,44,152,340,168,320,37,145,344,169,318,38,146,342,170,319,36,144,343,323,171,40,148,347,321,172,41,149,345,322,173,39,147,346,664,678,666,676,290,276,225,235,410,288,277,236,226,408,289,278,227,234,409,279,293,224,238,413,280,291,222,239,411,281,292,223,237,412,296,282,216,233,416,294,283,217,231,414,295,284,218,232,415,285,299,219,229,419,286,297,220,230,417,287,298,221,228,418,662,681,683,661,463,472,32,470,474,429,432,431,30,434,443,453,31,450,456,533,523,35,530,535,493,483,33,490,495,513,503,34,510,515,583,593,27,590,595,543,553,28,550,555,563,573,29,570,575,653,643,26,650,655,613,603,24,610,615,633,623,25,630,635,695,692,700,702,476,478,1,477,479,438,439,436,0,437,457,458,2,454,452,538,536,3,537,532,498,496,4,497,492,518,516,5,517,512,596,598,6,597,592,556,558,7,557,552,576,578,8,577,572,658,656,9,657,652,618,616,10,617,612,638,636,11,637,632,703,701,694,698,464,465,16,460,475,422,423,421,17,435,444,445,15,442,459,525,524,12,520,539,485,484,13,481,499,505,504,14,500,519,584,585,22,582,599,544,545,23,542,559,564,565,21,562,579,645,644,18,642,659,605,604,19,602,619,625,624,20,622,639,690,691,704,689,106,386,59,81,374,107,384,82,57,372,105,385,58,83,373,389,102,55,80,377,387,103,56,78,375,388,104,54,79,376,97,392,50,72,380,98,390,48,73,378,96,391,49,74,379,395,100,53,75,383,393,101,51,76,381,394,99,52,77,382,675,669,673,668,196,191,273,398,244,197,189,396,274,245,195,190,275,397,243,187,192,272,401,240,188,193,270,399,241,186,194,271,400,242,202,182,264,404,250,203,180,265,402,251,201,181,266,403,249,185,198,267,407,246,183,199,268,405,247,184,200,269,406,248,667,682,680,684,350,142,165,362,126,348,143,360,166,127,349,141,167,361,128,138,353,164,365,129,139,351,162,363,130,140,352,163,364,131,356,133,156,368,124,354,134,157,366,125,355,132,158,367,123,136,359,159,371,120,137,357,160,369,121,135,358,161,370,122,679,671,677,670,263,326,114,89,302,261,324,87,115,300,262,325,116,88,301,329,259,117,85,305,327,260,118,86,303,328,258,119,84,304,254,332,112,95,308,252,330,113,93,306,253,331,111,94,307,335,257,108,91,311,333,255,109,92,309,334,256,110,90,310,665,672,663,674 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#6da5e6765bc0adc27e9eb05052cc3d9b74fd6a5fdc541eafc0e7aaffee5eac36, 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 18:13:56 · history