Equation 677 Database

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Magma 406b2c3d6f71…

magma 406b2c3d6f71
Size
705
Isomorphism class hash
406b2c3d6f711ec4b1f78c2e1eb308113ea9f07de33d2ef95b9ee6195613c2f7
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 15:32:58
Display reorder
704,513,489,501,15,514,16,490,502,491,17,515,503,512,488,14,500,510,486,12,498,511,487,13,499,504,492,480,21,505,493,481,22,506,494,482,23,495,507,483,20,496,508,484,18,497,509,485,19,476,474,475,479,477,478,471,472,469,470,468,473,701,700,703,702,657,656,658,659,648,651,649,650,652,655,653,654,641,640,643,642,645,644,647,646,636,637,639,638,620,622,621,623,612,614,613,615,616,618,617,619,634,633,632,635,626,624,625,627,630,628,629,631,4,5,3,1,0,2,10,11,8,6,7,9,690,688,689,691,264,290,262,118,265,119,288,263,289,117,266,261,267,293,114,258,268,291,115,259,269,292,116,260,270,253,296,109,271,254,294,110,272,252,295,108,256,273,299,112,257,274,297,113,255,275,298,111,282,283,284,285,286,287,280,281,278,276,277,279,673,675,674,672,420,445,418,355,421,356,446,419,444,354,422,417,423,448,358,414,424,449,359,415,425,447,357,416,426,409,451,353,427,410,452,351,428,408,450,352,412,429,454,349,413,430,455,350,411,431,453,348,438,439,440,441,442,443,436,437,434,432,433,435,680,682,683,681,133,157,179,202,134,203,158,177,156,201,132,178,136,160,198,175,137,161,199,176,135,159,200,174,139,170,163,193,140,168,164,194,138,169,162,192,173,142,166,196,171,143,167,197,172,141,165,195,151,152,150,154,155,153,149,147,144,145,146,148,694,695,692,693,383,401,361,32,381,30,399,362,400,31,382,360,379,397,35,364,380,398,33,365,378,396,34,363,374,367,407,27,372,368,405,28,373,366,406,29,370,377,403,26,371,375,404,24,369,376,402,25,389,387,388,385,386,384,395,393,390,391,392,394,699,696,697,698,546,522,534,467,547,465,523,535,524,466,548,536,549,525,463,537,550,526,464,538,551,527,462,539,544,532,520,458,545,533,521,456,543,531,519,457,528,540,516,461,529,541,517,459,530,542,518,460,561,562,563,560,558,559,552,553,557,555,556,554,684,686,685,687,247,224,234,182,248,180,222,235,223,181,246,236,250,227,185,237,251,225,183,238,249,226,184,239,245,232,219,188,243,233,220,186,244,231,221,187,228,241,218,191,229,242,216,189,230,240,217,190,213,214,215,212,210,211,204,205,209,207,208,206,660,662,663,661,309,333,347,47,310,45,334,345,335,46,311,346,308,332,43,343,306,330,44,344,307,331,42,342,300,338,324,38,301,336,325,36,302,337,326,37,341,303,327,41,339,304,328,39,340,305,329,40,320,318,319,323,321,322,315,316,313,314,312,317,677,679,678,676,97,76,87,131,98,129,77,88,75,130,96,89,100,72,127,86,101,73,128,84,99,74,126,85,103,93,82,122,104,94,83,120,102,95,81,121,92,106,78,125,90,107,79,123,91,105,80,124,60,61,62,63,64,65,66,67,71,69,70,68,665,667,666,664,583,603,570,51,584,52,604,571,605,53,582,572,586,602,50,573,587,600,48,574,585,601,49,575,581,568,609,57,579,569,610,58,580,567,611,59,564,577,608,56,565,578,606,54,566,576,607,55,588,589,590,591,592,593,594,595,599,597,598,596,669,668,671,670 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#200706f015266953205238906f67170c94edeebe72a54762b43b1258f263dcc8, 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 15:33:00 · history