Equation 677 Database

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Magma 0e4d6f9f7900…

magma 0e4d6f9f7900
Size
705
Isomorphism class hash
0e4d6f9f790045f4cbc21c894a21d41d2da41af3b3a3859068801e732742478b
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 20:00:13
Display reorder
660,458,457,456,460,461,459,463,464,462,466,467,465,490,491,489,486,487,488,481,482,480,484,485,483,184,185,183,180,181,182,190,191,189,186,187,188,432,433,434,435,436,437,438,439,440,441,442,443,411,412,413,410,408,409,417,418,419,416,414,415,683,689,686,704,659,658,657,654,655,656,649,650,648,652,653,651,592,593,591,588,589,590,598,599,597,594,595,596,619,620,618,622,623,621,617,615,616,613,614,612,633,634,635,632,630,631,624,625,626,627,628,629,92,90,91,95,93,94,87,88,89,86,84,85,671,690,684,701,291,293,292,289,290,288,299,297,298,295,296,294,126,127,128,129,130,131,124,125,123,120,121,122,319,320,318,322,323,321,317,315,316,313,314,312,104,102,103,107,105,106,99,100,101,98,96,97,34,35,33,30,31,32,25,26,24,28,29,27,663,677,669,694,387,389,388,385,386,384,395,393,394,391,392,390,266,264,265,269,267,268,272,270,271,275,273,274,3,4,5,2,1,0,9,10,11,8,6,7,337,338,336,340,341,339,343,344,342,346,347,345,364,365,363,360,361,362,370,371,369,366,367,368,664,673,682,697,647,646,645,642,643,644,637,638,636,640,641,639,133,134,132,136,137,135,139,140,138,142,143,141,324,325,326,327,328,329,330,331,332,333,334,335,146,144,145,149,147,148,152,150,151,155,153,154,603,604,605,602,600,601,609,610,611,608,606,607,668,688,685,702,217,216,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,208,209,207,204,205,206,214,215,213,210,211,212,63,64,65,62,60,61,69,70,71,68,66,67,680,691,687,703,424,423,425,422,420,421,429,430,431,428,426,427,446,444,445,449,447,448,452,450,451,455,453,454,168,169,170,171,172,173,174,175,176,177,178,179,477,478,479,476,474,475,468,469,470,471,472,473,78,79,80,81,82,83,76,77,75,72,73,74,667,692,699,700,287,286,285,282,283,284,277,278,276,280,281,279,42,43,44,45,46,47,40,41,39,36,37,38,108,109,110,111,112,113,114,115,116,117,118,119,493,494,492,496,497,495,499,500,498,502,503,501,304,305,303,300,301,302,310,311,309,306,307,308,662,675,670,693,159,161,160,157,158,156,167,165,166,163,164,162,381,382,383,380,378,379,372,373,374,375,376,377,17,15,16,13,14,12,23,21,22,19,20,18,396,397,398,399,400,401,402,403,404,405,406,407,354,355,356,357,358,359,352,353,351,348,349,350,665,678,681,698,524,523,522,526,527,525,521,519,520,517,518,516,194,192,193,197,195,196,200,198,199,203,201,202,541,542,540,544,545,543,547,548,546,550,551,549,567,568,569,566,564,565,573,574,575,572,570,571,261,262,263,260,258,259,252,253,254,255,256,257,661,674,672,696,52,51,53,50,48,49,57,58,59,56,54,55,562,563,561,558,559,560,553,554,552,556,557,555,529,530,528,532,533,531,535,536,534,538,539,537,514,515,513,510,511,512,505,506,504,508,509,507,585,586,587,584,582,583,576,577,578,579,580,581,666,676,679,695 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {62} 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 20:00:14 · history