Equation 677 Database

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Magma 6f6c5fcf0883…

magma 6f6c5fcf0883
Size
705
Isomorphism class hash
6f6c5fcf088382b6208955fe0092dc42e09a28c490383c0aa364844a35a27756
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 15:19:35
Display reorder
704,395,561,549,587,550,562,585,393,394,563,551,586,391,560,548,583,392,558,546,584,390,559,547,582,540,578,552,386,541,576,553,384,542,577,554,385,581,543,555,389,579,544,556,387,580,545,557,388,572,570,571,575,573,574,567,568,565,566,564,569,663,661,660,662,128,148,189,177,190,149,178,126,127,147,191,179,131,144,188,176,129,145,186,174,130,146,187,175,180,168,154,123,181,169,155,124,182,170,153,125,171,183,150,122,172,184,151,120,173,185,152,121,164,162,163,167,165,166,159,160,157,158,156,161,689,690,691,688,611,435,423,411,424,436,412,609,610,437,425,413,607,434,422,410,608,432,420,408,606,433,421,409,429,417,441,602,430,418,442,600,431,419,443,601,416,428,440,605,414,426,438,603,415,427,439,604,398,396,397,401,399,400,404,402,406,407,405,403,669,670,671,668,34,229,217,205,218,230,206,35,33,228,216,204,30,232,220,208,31,233,221,209,32,231,219,207,223,211,235,25,224,212,236,26,222,210,234,24,214,226,238,28,215,227,239,29,213,225,237,27,196,197,195,192,193,194,202,203,200,198,199,201,677,679,678,676,102,250,286,274,287,251,275,103,104,249,285,273,105,246,282,270,106,247,283,271,107,248,284,272,277,265,241,100,278,266,242,101,276,264,240,99,268,280,244,96,269,281,245,97,267,279,243,98,258,259,260,261,262,263,256,257,254,252,253,255,665,667,666,664,659,658,656,657,649,650,648,651,655,654,652,653,643,642,640,641,647,646,644,645,639,638,636,637,620,621,622,623,612,613,614,615,616,617,618,619,633,632,634,635,624,625,626,627,629,628,630,631,593,591,592,589,590,588,599,597,594,595,596,598,694,693,692,695,45,69,57,93,58,70,94,46,47,71,59,95,44,68,56,92,42,66,54,90,43,67,55,91,48,84,60,36,49,85,61,37,50,86,62,38,87,51,63,39,88,52,64,40,89,53,65,41,80,78,79,83,81,82,75,76,73,74,72,77,702,701,700,703,115,313,306,288,307,314,289,116,114,312,308,290,118,316,309,291,119,317,310,292,117,315,311,293,304,294,319,113,305,295,320,111,303,296,318,112,297,300,322,109,298,301,323,110,299,302,321,108,329,327,328,325,326,324,335,333,330,331,332,334,698,697,696,699,14,533,518,510,516,531,511,12,13,532,517,512,17,529,521,513,15,530,519,514,16,528,520,515,524,508,539,20,522,509,537,18,523,507,538,19,504,527,535,23,505,525,536,21,506,526,534,22,495,496,497,494,492,493,501,502,499,500,498,503,673,674,675,672,138,362,349,337,350,360,338,139,140,361,348,336,141,365,352,340,142,363,353,341,143,364,351,339,355,343,368,136,356,344,366,137,354,342,367,135,346,358,371,132,347,359,369,133,345,357,370,134,373,374,372,376,377,375,379,380,381,382,383,378,683,682,680,681,3,463,455,480,453,464,481,4,5,462,454,482,2,466,451,483,1,467,452,484,0,465,450,485,446,486,461,9,444,487,459,10,445,488,460,11,489,449,457,8,490,447,458,6,491,448,456,7,469,470,468,472,473,471,475,476,477,478,479,474,687,685,684,686 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#14697465b8cd7575930ebcd6f1cfb0d098649f4474b7abfd50cfc1485faac906, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 15:19:38 · history