Equation 677 Database

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Magma 0a94f4ae5d5f…

magma 0a94f4ae5d5f
Size
705
Isomorphism class hash
0a94f4ae5d5fbb41047fcf30f8d9def211439ed8a4ba4c5e5a1e8d61133e91e3
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 16:31:48
Display reorder
660,115,615,606,611,614,116,634,635,626,631,114,654,655,646,651,118,595,594,586,591,119,555,554,546,551,117,575,574,566,571,113,433,432,426,429,111,455,454,446,451,112,475,474,466,471,495,109,494,486,491,506,515,110,514,511,535,108,534,526,531,688,686,700,701,10,617,613,601,616,11,636,637,633,621,9,656,657,653,640,6,597,596,593,580,7,557,556,553,541,8,577,576,573,561,0,435,434,431,424,2,457,456,453,441,1,477,476,473,460,497,4,496,493,480,513,517,5,516,500,537,3,536,533,520,699,694,702,703,48,417,369,345,393,49,394,418,370,346,50,395,419,371,347,51,416,392,368,344,52,414,390,366,342,53,415,391,367,343,54,408,384,360,336,55,409,385,361,337,56,410,386,362,338,411,57,387,363,339,364,412,58,388,340,413,59,389,365,341,669,667,675,681,140,405,309,381,273,138,274,406,310,382,139,275,407,311,383,143,404,272,308,380,141,402,270,306,378,142,403,271,307,379,135,396,264,300,372,136,397,265,301,373,137,398,266,302,374,399,134,267,303,375,304,400,132,268,376,401,133,269,305,377,670,672,661,678,154,619,612,608,604,155,624,639,632,628,153,644,659,652,648,150,599,584,592,588,151,559,544,552,548,152,579,564,572,568,145,439,425,430,427,146,459,444,452,448,144,479,464,472,468,499,148,484,492,488,512,519,149,504,508,539,147,524,532,528,698,692,689,695,82,609,607,605,603,83,623,629,627,625,81,643,649,647,645,78,589,583,587,585,79,549,543,547,545,80,569,563,567,565,73,438,420,422,421,74,449,443,447,445,72,469,463,467,465,489,76,483,487,485,507,509,77,503,505,529,75,523,527,525,691,687,696,693,91,602,610,618,600,92,620,622,630,638,90,641,642,650,658,94,582,581,590,598,95,542,540,550,558,93,562,560,570,578,89,437,423,428,436,87,442,440,450,458,88,462,461,470,478,482,85,481,490,498,510,502,86,501,518,522,84,521,530,538,690,704,697,685,262,164,297,190,202,263,203,162,298,191,261,201,163,299,189,258,167,198,296,186,259,165,199,294,187,260,166,200,295,188,253,159,193,288,181,254,160,194,289,182,252,161,192,290,180,158,256,196,291,184,292,156,257,197,185,157,255,195,293,183,664,679,662,673,107,285,69,28,46,105,47,286,70,29,106,45,287,71,27,103,284,42,68,24,104,282,43,66,25,102,283,44,67,26,98,276,37,60,34,96,277,38,61,35,97,278,36,62,33,279,101,40,63,30,64,280,99,41,31,281,100,39,65,32,677,671,683,663,124,318,15,333,357,125,358,319,16,334,123,359,320,17,335,120,321,356,14,332,121,322,354,12,330,122,323,355,13,331,130,316,348,21,324,131,317,349,22,325,129,315,350,23,326,312,126,351,20,327,18,313,127,352,328,314,128,353,19,329,682,666,668,684,176,239,245,209,218,174,216,237,243,207,175,217,238,244,208,179,235,221,241,205,177,236,219,242,206,178,234,220,240,204,171,230,224,251,215,172,228,222,249,213,173,229,223,250,214,233,170,227,247,211,248,231,168,225,212,232,169,226,246,210,680,676,665,674 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#34f20f8c77c0cbdeb0b8c0e60587a50e7d9ef4f1dbdd588ea7161aafd1a43efd, 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 16:31:49 · history