Equation 677 Database

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Magma fdaf787285a1…

magma fdaf787285a1
Size
705
Isomorphism class hash
fdaf787285a1b4e960cd8ca51eaed4af8be6ec4dd8f3773ebf780094a3fe16c2
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 20:42:43
Display reorder
704,515,26,481,499,513,24,500,482,514,25,498,480,29,511,484,502,27,512,485,503,510,28,501,483,32,506,487,497,504,30,495,488,505,31,496,486,35,509,490,493,507,33,494,491,508,34,492,489,479,477,478,475,476,474,470,468,472,473,471,469,701,702,700,703,658,657,656,659,650,648,651,649,654,652,655,653,640,642,641,643,645,646,644,647,638,636,639,637,620,622,621,623,614,612,615,613,617,616,618,619,632,633,634,635,624,625,627,626,629,628,631,630,70,71,69,66,67,68,61,62,63,64,65,60,689,690,688,691,321,232,290,306,322,233,307,288,323,231,308,289,228,320,293,309,229,318,291,310,319,230,311,292,238,312,296,304,313,239,305,294,314,237,303,295,234,315,299,300,316,235,301,297,317,236,302,298,332,330,331,335,333,334,327,328,325,326,324,329,674,673,675,672,390,413,364,383,391,411,381,365,392,412,382,363,409,393,360,379,410,394,361,380,395,408,378,362,419,388,370,374,389,417,372,371,387,418,373,369,415,384,366,377,385,416,375,367,386,414,376,368,356,354,355,359,357,358,351,352,349,350,348,353,683,680,682,681,139,37,158,175,140,38,176,156,138,36,174,157,40,142,161,178,41,143,159,179,141,39,177,160,43,137,164,173,135,44,171,162,136,42,172,163,46,133,167,169,134,47,170,165,132,45,168,166,154,155,153,150,151,152,145,146,147,148,149,144,692,694,695,693,425,396,451,460,423,397,461,452,424,398,459,450,399,421,454,456,400,422,455,457,420,401,458,453,402,431,449,466,429,403,467,447,430,404,465,448,405,427,445,462,428,406,463,446,426,407,464,444,433,434,432,436,437,435,439,440,441,442,443,438,697,699,696,698,547,73,521,537,548,74,538,519,546,72,539,520,76,550,517,536,77,551,518,534,549,75,535,516,79,545,527,528,543,80,529,525,544,78,530,526,82,541,523,531,542,83,532,524,540,81,533,522,563,561,562,559,560,558,554,552,556,557,555,553,685,687,686,684,202,8,219,188,203,6,186,220,201,7,187,221,11,198,218,191,9,199,216,189,200,10,190,217,3,193,225,183,194,4,184,226,192,5,185,227,2,196,224,182,197,1,180,222,195,0,181,223,211,212,210,214,215,213,209,207,204,205,206,208,663,660,662,661,286,336,254,271,287,337,272,252,285,338,270,253,339,282,257,274,340,283,255,275,284,341,273,256,342,277,260,269,278,343,267,258,276,344,268,259,345,280,263,265,281,346,266,261,279,347,264,262,250,251,249,246,247,248,241,242,243,244,245,240,678,677,679,676,103,48,121,95,104,49,93,122,102,50,94,120,51,106,124,91,52,107,125,92,105,53,90,123,54,101,127,86,99,55,84,128,100,56,85,126,57,97,130,89,98,58,87,131,96,59,88,129,118,119,117,114,115,116,109,110,111,112,113,108,667,664,666,665,586,21,603,572,587,22,570,604,585,23,571,605,20,582,602,575,18,583,600,573,584,19,574,601,12,577,609,567,578,13,568,610,576,14,569,611,15,580,608,566,581,16,564,606,579,17,565,607,594,595,596,597,598,599,592,593,590,588,589,591,671,669,668,670 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#cce41c1fd55a940f76617a374756c8d0de5f99032cd8fe3feeb0eb2c48843df6, 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 20:42:44 · history