Equation 677 Database

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Magma 5955e245519e…

magma 5955e245519e
Size
705
Isomorphism class hash
5955e245519e29dac1f82ea3c513274be7a3b358f984bc13177a95f8baf0712a
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 15:22:59
Display reorder
660,521,538,46,529,531,480,47,489,491,498,501,518,45,509,511,455,448,42,449,450,475,460,43,467,468,435,421,44,427,428,37,640,658,649,651,601,618,609,38,611,620,638,629,36,631,578,561,569,40,571,598,581,589,41,591,558,540,549,39,551,696,691,686,701,524,536,237,523,525,484,238,483,485,496,504,516,239,503,505,453,442,236,441,443,473,463,234,462,464,433,423,235,422,424,228,644,656,643,645,604,616,603,229,605,624,636,623,230,625,576,564,563,231,565,596,584,583,232,585,556,544,543,233,545,700,688,689,697,133,281,204,87,118,134,205,88,119,279,132,280,206,89,117,277,136,207,86,114,278,137,208,84,115,276,135,209,85,116,210,139,287,93,109,140,285,94,211,110,138,286,95,212,108,283,142,92,213,112,284,143,90,214,113,282,141,91,215,111,674,666,670,664,401,60,14,389,6,399,12,387,7,61,400,62,13,388,8,63,397,17,385,9,64,398,15,386,10,65,396,16,384,11,20,407,66,395,4,405,67,393,18,5,406,68,394,19,3,69,403,391,23,1,70,404,392,21,0,71,402,390,22,2,681,675,682,683,526,530,216,532,534,486,217,492,494,490,506,510,218,512,514,456,447,219,451,452,478,465,220,469,471,436,425,221,429,431,222,646,650,652,654,606,610,612,223,614,626,630,632,224,634,570,566,572,225,574,590,586,592,226,594,550,546,552,227,554,692,703,694,702,522,537,24,527,539,482,25,487,499,497,502,517,26,507,519,454,458,27,457,459,474,477,28,476,479,434,438,29,437,439,30,642,657,647,659,602,617,607,31,619,622,637,627,32,639,577,562,567,33,579,597,582,587,34,599,557,542,547,35,559,685,690,698,699,533,528,77,520,535,493,75,481,495,488,513,508,76,500,515,444,445,73,440,446,466,470,74,461,472,426,430,72,420,432,83,653,648,641,655,613,608,600,81,615,633,628,621,82,635,568,573,560,79,575,588,593,580,80,595,548,553,541,78,555,704,695,693,687,269,377,106,257,244,267,107,255,245,375,268,376,105,256,243,373,265,102,253,240,374,266,103,254,241,372,264,104,252,242,97,275,383,263,250,273,381,261,98,251,274,382,262,96,249,379,271,259,100,246,380,272,260,101,247,378,270,258,99,248,661,680,663,678,317,413,130,49,164,315,131,50,162,411,316,412,129,48,163,409,313,126,52,167,410,314,127,53,165,408,312,128,51,166,121,323,419,55,159,321,417,56,122,160,322,418,54,120,161,415,319,58,124,158,416,320,59,125,156,414,318,57,123,157,672,679,668,684,341,293,195,329,353,339,196,327,351,291,340,292,197,328,352,289,337,194,325,349,290,338,192,326,350,288,336,193,324,348,201,347,299,335,359,345,297,333,202,357,346,298,334,203,358,295,343,331,200,355,296,344,332,198,356,294,342,330,199,354,669,676,673,665,184,168,144,305,365,185,145,303,363,169,183,170,146,304,364,171,180,147,301,361,172,181,148,302,362,173,182,149,300,360,150,190,174,311,371,191,175,309,151,369,189,176,310,152,370,177,186,307,153,367,178,187,308,154,368,179,188,306,155,366,667,677,671,662 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#164604ba66664ae7e7b126fe65d39300d84fb27e5ce614035873663e987c6567, 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 15:23:01 · history