Equation 677 Database

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Magma f51d7f864130…

magma f51d7f864130
Size
705
Isomorphism class hash
f51d7f86413064eeadacc2fcadf5665f337a726d2129b96a22c39e7285a2f545
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 19:58:32
Display reorder
660,241,240,242,243,244,245,246,247,248,249,250,251,274,275,273,270,271,272,265,266,264,268,269,267,254,252,253,257,255,256,260,258,259,263,261,262,169,170,168,172,173,171,175,176,174,178,179,177,232,233,231,228,229,230,238,239,237,234,235,236,694,681,696,703,121,120,122,123,124,125,126,127,128,129,130,131,98,96,97,101,99,100,104,102,103,107,105,106,132,133,134,135,136,137,138,139,140,141,142,143,452,450,451,455,453,454,447,448,449,446,444,445,112,113,111,108,109,110,118,119,117,114,115,116,686,688,698,701,478,477,479,476,474,475,468,469,470,471,472,473,499,500,498,502,503,501,497,495,496,493,494,492,480,481,482,483,484,485,486,487,488,489,490,491,151,152,150,154,155,153,149,147,148,145,146,144,457,458,456,460,461,459,463,464,462,466,467,465,671,666,675,689,383,382,381,378,379,380,373,374,372,376,377,375,399,400,401,398,396,397,405,406,407,404,402,403,389,387,388,385,386,384,395,393,394,391,392,390,339,340,341,338,336,337,345,346,347,344,342,343,361,362,360,364,365,363,367,368,366,370,371,369,667,664,674,693,548,547,546,550,551,549,545,543,544,541,542,540,509,507,508,505,506,504,515,513,514,511,512,510,521,519,520,517,518,516,527,525,526,523,524,522,539,537,538,535,536,534,530,528,529,533,531,532,28,29,27,24,25,26,34,35,33,30,31,32,687,682,697,700,617,616,615,612,613,614,622,623,621,618,619,620,636,637,638,639,640,641,642,643,644,645,646,647,625,626,624,628,629,627,631,632,630,634,635,633,0,2,1,4,5,3,7,8,6,10,11,9,653,651,652,649,650,648,659,657,658,655,656,654,684,680,695,704,305,304,303,300,301,302,310,311,309,306,307,308,321,322,323,320,318,319,312,313,314,315,316,317,335,333,334,331,332,330,326,324,325,329,327,328,283,284,282,286,287,285,281,279,280,277,278,276,296,294,295,299,297,298,291,292,293,290,288,289,685,683,699,702,415,414,416,417,418,419,412,413,411,408,409,410,441,442,443,440,438,439,432,433,434,435,436,437,426,427,428,429,430,431,424,425,423,420,421,422,354,355,356,357,358,359,352,353,351,348,349,350,17,15,16,13,14,12,23,21,22,19,20,18,668,663,673,692,607,606,608,609,610,611,604,605,603,600,601,602,58,59,57,54,55,56,49,50,48,52,53,51,42,43,44,45,46,47,40,41,39,36,37,38,95,93,94,91,92,90,86,84,85,89,87,88,67,68,66,70,71,69,65,63,64,61,62,60,670,662,677,690,193,192,194,195,196,197,198,199,200,201,202,203,226,227,225,222,223,224,217,218,216,220,221,219,206,204,205,209,207,208,212,210,211,215,213,214,166,167,165,162,163,164,157,158,156,160,161,159,184,185,183,180,181,182,190,191,189,186,187,188,669,661,676,679,599,598,597,594,595,596,589,590,588,592,593,591,569,567,568,565,566,564,575,573,574,571,572,570,560,558,559,563,561,562,555,556,557,554,552,553,76,77,75,72,73,74,82,83,81,78,79,80,578,576,577,581,579,580,584,582,583,587,585,586,672,665,678,691 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 = {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 19:58:33 · history