Equation 677 Database

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Magma 283f1fe20ba1…

magma 283f1fe20ba1
Size
705
Isomorphism class hash
283f1fe20ba16366cf1858515c068c9f26e87824394152786fee7d9388725fa3
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 20:38:04
Display reorder
660,534,9,538,530,535,494,10,498,490,495,514,11,518,510,515,8,453,455,452,454,6,471,475,468,472,7,431,435,428,432,654,658,1,650,655,614,618,0,610,615,634,638,2,630,635,578,574,3,570,575,598,594,4,590,595,558,554,5,550,555,691,697,696,701,537,41,521,532,526,497,39,480,492,486,517,40,501,512,506,37,447,441,444,442,38,474,460,469,466,36,434,421,429,426,657,640,47,652,646,617,601,45,612,606,637,620,46,632,626,561,577,43,572,566,581,597,44,592,586,540,557,42,552,546,692,686,700,695,139,281,53,113,145,140,279,51,111,146,138,280,52,112,144,277,142,49,109,148,278,143,50,110,149,276,141,48,108,147,137,59,287,119,151,135,57,285,117,152,136,58,286,118,150,55,133,283,115,154,56,134,284,116,155,54,132,282,114,153,672,662,668,666,377,235,341,401,365,375,236,339,399,363,376,234,340,400,364,238,373,337,397,361,239,374,338,398,362,237,372,336,396,360,383,347,233,407,371,381,345,231,405,369,382,346,232,406,370,343,379,229,403,367,344,380,230,404,368,342,378,228,402,366,682,676,678,671,524,187,523,522,525,484,188,483,482,485,504,186,503,502,505,190,450,449,448,451,191,464,463,462,465,189,424,423,422,425,644,643,185,642,645,604,603,183,602,605,624,623,184,622,625,563,564,181,562,565,583,584,182,582,585,543,544,180,542,545,703,698,694,702,527,81,529,531,539,487,83,489,491,499,507,78,509,511,519,80,457,456,458,459,82,477,476,478,479,79,437,436,438,439,647,649,77,651,659,607,609,75,611,619,627,629,76,631,639,569,567,73,571,579,589,587,74,591,599,549,547,72,551,559,689,690,687,685,536,30,528,520,533,496,31,488,481,493,516,32,508,500,513,33,446,443,440,445,34,473,467,461,470,35,433,427,420,430,656,648,28,641,653,616,608,29,600,613,636,628,27,621,633,568,576,24,560,573,588,596,25,580,593,548,556,26,541,553,704,693,699,688,174,102,224,199,158,175,103,222,200,156,176,104,223,198,157,105,177,227,202,161,106,178,225,203,159,107,179,226,201,160,172,219,100,197,164,173,220,101,195,162,171,221,99,196,163,218,168,96,193,167,216,169,97,194,165,217,170,98,192,166,675,681,670,677,353,66,413,269,329,351,67,411,267,327,352,68,412,268,328,69,349,409,265,325,70,350,410,266,326,71,348,408,264,324,359,419,64,275,335,357,417,65,273,333,358,418,63,274,334,415,355,60,271,331,416,356,61,272,332,414,354,62,270,330,679,669,674,684,389,122,293,317,305,387,120,291,315,303,388,121,292,316,304,125,385,289,313,301,123,386,290,314,302,124,384,288,312,300,395,299,128,323,311,393,297,126,321,309,394,298,127,322,310,295,391,131,319,307,296,392,129,320,308,294,390,130,318,306,667,665,680,663,208,20,261,244,92,209,18,262,245,90,207,19,263,243,91,23,204,260,240,95,21,205,258,241,93,22,206,259,242,94,214,252,15,250,87,215,253,16,251,88,213,254,17,249,89,255,210,14,246,86,256,211,12,247,84,257,212,13,248,85,673,683,664,661 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#c84e71ca0bd6781f4c1c1e66d375057eb5ddb823e6cd89140cc4ca3da0f421d2, 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 20:38:05 · history