Equation 677 Database

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Magma 02d59b637365…

magma 02d59b637365
Size
705
Isomorphism class hash
02d59b637365da57f50ada1ac6c6afa9c61b633ca3f183c81de89bc089b35a56
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 17:33:02
Display reorder
660,570,572,33,560,574,34,590,580,594,592,35,552,550,541,554,630,32,632,621,634,30,650,652,640,654,31,610,612,601,614,24,530,532,523,534,25,490,492,483,494,26,510,512,503,514,444,27,445,441,446,468,28,470,461,472,420,428,29,430,432,692,697,689,687,576,571,44,575,565,42,596,595,585,591,43,551,556,555,545,636,47,631,635,625,45,656,651,655,645,46,616,611,615,605,39,536,531,535,525,40,496,491,495,485,41,516,511,515,505,456,38,454,447,442,474,36,469,473,464,433,434,37,429,424,702,695,685,696,175,53,307,224,197,308,176,222,195,51,306,52,174,223,196,178,310,49,227,193,311,179,50,225,194,309,177,48,226,192,305,173,59,219,203,303,171,57,220,201,304,172,58,221,202,169,301,55,218,199,170,302,56,216,200,217,168,300,54,198,662,674,680,678,391,343,6,108,331,7,392,109,332,344,8,342,390,110,330,394,9,346,111,334,10,395,347,112,335,11,393,345,113,333,4,389,341,114,329,5,387,339,115,327,3,388,340,116,328,385,1,337,117,325,386,0,338,118,326,119,384,2,336,324,666,679,668,673,563,578,215,568,566,213,583,588,586,598,214,558,543,548,546,623,211,638,628,626,212,643,658,648,646,210,603,618,608,606,206,522,538,528,526,204,482,498,488,486,205,502,518,508,506,440,209,449,453,452,462,207,476,466,465,426,422,208,436,425,704,691,699,693,564,573,86,579,562,84,584,599,582,593,85,553,544,559,542,624,89,633,639,622,87,644,653,659,642,88,604,613,619,602,92,524,533,539,520,90,484,493,499,481,91,504,513,519,501,451,95,455,457,450,463,93,471,477,460,437,423,94,431,421,694,701,690,703,567,561,98,569,577,96,587,589,597,581,97,540,547,549,557,627,101,620,629,637,99,647,641,649,657,100,607,600,609,617,104,527,521,529,537,102,487,480,489,497,103,507,500,509,517,458,107,459,443,448,479,105,478,467,475,427,438,106,439,435,698,700,688,686,319,367,189,237,379,190,320,238,380,368,191,366,318,239,378,322,188,370,236,382,186,323,371,234,383,187,321,369,235,381,180,317,365,228,377,181,315,363,229,375,182,316,364,230,376,313,183,361,231,373,314,184,362,232,374,233,312,185,360,372,672,665,670,661,274,253,60,277,298,61,275,278,299,254,62,252,273,276,297,270,63,256,280,294,64,271,257,281,295,65,272,255,279,296,66,265,259,283,289,67,266,260,284,290,68,264,258,282,288,268,69,262,286,292,269,70,263,287,293,285,267,71,261,291,684,664,682,676,130,403,157,133,355,158,131,134,356,404,156,402,129,132,354,126,160,406,136,358,161,127,407,137,359,159,128,405,135,357,163,121,401,139,353,164,122,399,140,351,162,120,400,138,352,124,166,397,142,349,125,167,398,143,350,141,123,165,396,348,669,683,675,681,78,147,18,415,246,19,79,416,247,148,20,149,80,414,248,81,21,146,418,249,22,82,144,419,250,23,83,145,417,251,16,76,153,413,244,17,77,154,411,245,15,75,155,412,243,72,12,152,409,240,73,13,150,410,241,408,74,14,151,242,671,677,667,663 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#58acf36cbe6044882516075a72a3c87dd19ad7333778c9b60a583a8d5c85fb41, 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 17:33:03 · history