Equation 677 Database

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Magma feb7e0dc9055…

magma feb7e0dc9055
Size
705
Isomorphism class hash
feb7e0dc90558821f1a0f3dd1f5a54dd5c79bed9d9636ee4a1566ec26a9fae1f
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 19:57:43
Display reorder
660,123,564,578,575,572,124,584,598,595,592,125,544,558,555,552,624,122,638,635,632,644,120,658,655,652,604,121,618,615,612,129,524,538,535,532,130,484,498,495,492,131,504,518,515,512,442,128,449,448,446,464,126,476,473,470,424,127,436,433,430,691,689,693,698,106,567,561,570,566,107,587,580,590,586,105,547,541,550,546,627,102,621,630,626,647,103,640,650,646,607,104,601,610,606,97,527,520,530,526,98,487,480,490,486,96,507,500,510,506,452,100,450,445,444,467,101,460,468,466,427,99,420,428,426,702,699,695,697,76,206,178,34,198,77,204,179,35,199,75,205,177,33,200,209,72,174,30,201,207,73,175,31,202,208,74,176,32,203,82,212,169,25,196,83,210,170,26,197,81,211,168,24,195,215,78,172,28,192,213,79,173,29,193,214,80,171,27,194,662,677,670,664,45,295,403,242,355,46,296,404,240,356,47,294,402,241,354,298,44,406,245,358,299,42,407,243,359,297,43,405,244,357,36,293,401,248,353,37,291,399,246,351,38,292,400,247,352,289,39,397,251,349,290,40,398,249,350,288,41,396,250,348,669,675,665,680,112,574,560,576,577,113,594,581,596,597,111,554,540,556,557,634,108,620,636,637,654,109,641,656,657,614,110,600,616,617,118,534,521,536,537,119,494,481,496,497,117,514,501,516,517,447,114,440,455,456,472,115,461,474,475,432,116,422,434,435,704,696,690,692,12,571,563,573,579,13,591,583,593,599,14,551,543,553,559,631,15,623,633,639,651,16,643,653,659,611,17,603,613,619,18,531,523,533,539,19,491,483,493,499,20,511,503,513,519,453,21,451,454,457,469,22,463,471,477,429,23,423,431,437,687,701,688,703,230,568,569,565,562,228,588,589,585,582,229,548,549,545,542,628,233,629,625,622,648,231,649,645,642,608,232,609,605,602,236,528,529,525,522,234,488,489,485,482,235,508,509,505,502,459,239,458,443,441,479,237,478,465,462,438,238,439,425,421,700,686,694,685,162,92,343,379,0,163,90,344,380,2,164,91,342,378,1,95,165,346,382,4,93,166,347,383,5,94,167,345,381,3,160,87,341,377,7,161,88,339,375,8,159,89,340,376,6,86,156,337,373,10,84,157,338,374,11,85,158,336,372,9,678,674,681,673,70,49,415,259,283,71,50,416,260,284,69,48,414,258,282,52,66,418,262,286,53,67,419,263,287,51,68,417,261,285,61,55,413,257,281,62,56,411,255,279,60,54,412,256,280,58,64,409,253,277,59,65,410,254,278,57,63,408,252,276,684,663,672,682,222,367,150,391,183,223,368,151,392,184,224,366,152,390,185,370,225,153,394,182,371,226,154,395,180,369,227,155,393,181,220,365,148,389,189,221,363,149,387,190,219,364,147,388,191,361,216,144,385,188,362,217,145,386,186,360,218,146,384,187,679,683,676,671,132,307,331,271,319,133,308,332,272,320,134,306,330,270,318,310,135,334,274,322,311,136,335,275,323,309,137,333,273,321,138,305,329,269,317,139,303,327,267,315,140,304,328,268,316,301,141,325,265,313,302,142,326,266,314,300,143,324,264,312,661,667,666,668 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#b82bea23d952545bcb5d6b6a0cc235694bb3bc5cc3b3a153b6c38e307d02b955, 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 19:57:44 · history