Equation 677 Database

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Magma 2b810b2fd38a…

magma 2b810b2fd38a
Size
705
Isomorphism class hash
2b810b2fd38a1c40deefaae577f71ddfc934514a51315fa62129df5f6a6b5ed1
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 19:13:46
Display reorder
660,630,109,637,629,635,650,110,657,649,655,610,108,617,609,615,112,550,557,549,555,113,570,577,569,575,111,590,597,589,595,451,115,455,450,454,470,116,477,469,475,114,430,437,429,435,118,510,517,509,515,119,530,537,529,535,117,490,497,489,495,689,697,690,701,633,246,638,627,628,653,247,658,647,648,613,248,618,607,608,249,553,558,547,548,250,573,578,567,568,251,593,598,587,588,453,244,456,448,449,473,245,478,467,468,243,433,438,427,428,240,513,518,507,508,241,533,538,527,528,242,493,498,487,488,700,688,695,702,318,231,334,406,286,319,232,335,407,287,320,233,333,405,285,230,321,330,402,282,228,322,331,403,283,229,323,332,404,284,316,237,325,397,277,317,238,326,398,278,239,315,324,396,276,236,312,328,400,280,234,313,329,401,281,235,314,327,399,279,681,664,677,668,382,69,370,394,94,383,70,371,395,95,381,71,369,393,93,68,378,366,390,90,66,379,367,391,91,67,380,368,392,92,373,60,361,385,85,374,61,362,386,86,62,372,360,384,84,63,376,364,388,88,64,377,365,389,89,65,375,363,387,87,674,666,672,670,639,171,625,626,624,659,172,645,646,644,619,173,605,606,604,170,559,545,546,544,168,579,565,566,564,169,599,585,586,584,459,177,446,447,445,479,178,465,466,464,179,439,425,426,424,176,519,505,506,504,174,539,525,526,524,175,499,485,486,484,692,703,686,698,636,135,620,631,634,656,136,641,651,654,616,137,600,611,614,134,556,540,551,554,132,576,561,571,574,133,596,581,591,594,458,141,440,441,442,476,142,460,471,474,143,436,421,431,434,140,516,500,511,514,138,536,520,531,534,139,496,481,491,494,691,696,699,693,622,144,632,623,621,642,145,652,643,640,602,146,612,603,601,147,542,552,543,541,148,562,572,563,560,149,582,592,583,580,457,150,452,443,444,461,151,472,462,463,152,422,432,423,420,153,502,512,503,501,154,522,532,523,521,155,482,492,483,480,694,704,685,687,226,48,162,3,200,227,49,163,4,198,225,50,164,5,199,51,222,165,2,203,52,223,166,1,201,53,224,167,0,202,217,54,160,9,195,218,55,161,10,196,56,216,159,11,197,57,220,156,8,194,58,221,157,6,192,59,219,158,7,193,673,675,661,662,96,124,72,20,310,97,125,73,18,311,98,123,74,19,309,120,99,75,23,306,121,100,76,21,307,122,101,77,22,308,102,130,78,15,301,103,131,79,16,302,129,104,80,17,300,126,105,81,14,304,127,106,82,12,305,128,107,83,13,303,671,667,682,676,25,341,261,274,358,26,339,262,275,359,24,340,263,273,357,337,28,260,270,354,338,29,258,271,355,336,27,259,272,356,31,347,252,265,349,32,345,253,266,350,346,30,254,264,348,343,34,255,268,352,344,35,256,269,353,342,33,257,267,351,663,669,680,684,180,38,298,418,210,181,36,299,419,211,182,37,297,417,212,41,183,294,414,213,39,184,295,415,214,40,185,296,416,215,186,44,289,409,208,187,42,290,410,209,43,188,288,408,207,47,189,292,412,204,45,190,293,413,205,46,191,291,411,206,683,679,678,665 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#954a2425e38b1f8d73f83d01c811c18c22a6cf13713c169e64792ee66a752510, 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 19:13:47 · history