Equation 677 Database

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Magma 3872adc9eb02…

magma 3872adc9eb02
Size
705
Isomorphism class hash
3872adc9eb02a693dee15c88bf1bda5818bcad760595067576242078ba771de7
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 15:30:52
Display reorder
660,67,604,609,610,616,636,624,68,629,630,656,644,66,649,650,596,70,584,589,590,71,556,544,549,550,576,69,564,569,570,65,426,435,429,430,63,444,456,449,450,64,464,476,469,470,484,61,496,489,490,509,504,62,516,510,524,60,536,529,530,690,700,692,691,88,615,611,617,608,628,635,89,631,637,648,655,87,651,657,588,84,595,591,597,85,548,555,551,557,568,86,575,571,577,94,434,428,431,436,95,455,448,451,457,93,475,468,471,477,495,90,488,491,497,511,515,91,508,517,535,92,528,531,537,699,695,701,693,9,381,405,321,113,111,382,10,406,322,112,383,11,407,323,109,8,380,404,320,6,110,378,402,318,108,7,379,403,319,1,372,119,396,312,0,373,117,397,313,2,374,118,398,314,375,3,115,399,315,400,376,4,116,316,377,5,114,401,317,674,670,666,678,221,247,273,417,357,358,248,219,274,418,359,246,220,275,419,356,217,250,272,416,218,354,251,270,414,355,216,249,271,415,227,245,348,264,408,225,243,349,265,409,226,244,350,266,410,241,223,351,267,411,268,242,224,352,412,240,222,353,269,413,677,669,683,663,103,619,600,603,614,634,639,104,620,623,654,659,102,640,643,594,106,599,581,583,107,554,559,540,543,574,105,579,560,563,101,439,433,424,425,99,459,454,440,443,100,479,474,460,463,499,97,494,482,483,502,519,98,514,503,539,96,534,522,523,687,697,686,703,153,607,612,601,605,625,627,154,632,621,645,647,155,652,641,585,152,587,592,580,150,545,547,552,541,565,151,567,572,561,144,438,421,422,420,145,447,445,452,441,146,467,465,472,461,487,147,485,492,480,512,507,148,505,500,527,149,525,532,521,689,685,702,694,164,618,613,606,602,622,638,162,633,626,642,658,163,653,646,582,167,598,593,586,165,542,558,553,546,562,166,578,573,566,159,437,423,432,427,160,458,442,453,446,161,478,462,473,466,498,158,481,493,486,513,518,156,501,506,538,157,520,533,526,704,698,688,696,209,333,261,297,281,279,334,207,262,298,280,335,208,263,299,277,205,332,260,296,206,278,330,258,294,276,204,331,259,295,215,324,287,252,288,213,325,285,253,289,214,326,286,254,290,327,211,283,255,291,256,328,212,284,292,329,210,282,257,293,667,661,664,662,56,309,345,141,122,120,310,54,346,142,121,311,55,347,143,125,59,308,344,140,57,123,306,342,138,124,58,307,343,139,51,300,128,336,132,52,301,126,337,133,53,302,127,338,134,303,50,131,339,135,340,304,48,129,136,305,49,130,341,137,665,682,675,668,234,32,36,80,369,370,30,235,37,78,371,31,236,38,79,368,237,35,39,83,238,366,33,40,81,367,239,34,41,82,232,27,360,42,75,233,28,361,43,76,231,29,362,44,77,26,228,363,45,74,46,24,229,364,72,25,230,365,47,73,673,671,684,681,19,197,393,184,172,173,195,20,394,185,171,196,18,395,183,168,22,193,392,180,23,169,194,390,181,170,21,192,391,182,17,203,178,384,190,15,201,179,385,191,16,202,177,386,189,199,13,174,387,186,388,200,14,175,187,198,12,176,389,188,672,679,680,676 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#1d08ed48a203bbb312f14b36e229a5f315d68c29c0949a9ef7235ea8d2bd9766, 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 15:30:53 · history