Equation 677 Database

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Magma f1aac7fb8fbe…

magma f1aac7fb8fbe
Size
705
Isomorphism class hash
f1aac7fb8fbebb0c3225670593fdee6326c9d541d07a270b823525fc149155a6
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 19:47:31
Display reorder
704,534,13,516,506,535,14,517,504,536,12,518,505,537,16,519,509,538,17,520,507,539,15,521,508,19,532,512,522,20,533,510,523,18,531,511,524,22,528,515,525,23,529,513,526,21,530,514,527,540,541,542,543,544,545,546,547,551,549,550,548,660,663,661,662,282,60,264,253,283,61,265,254,284,62,266,252,285,63,267,256,286,64,268,257,287,65,269,255,66,280,259,270,67,281,260,271,68,279,258,272,69,276,262,273,70,277,263,274,71,278,261,275,245,243,244,241,242,240,251,249,246,247,248,250,691,689,690,688,571,403,553,591,572,404,554,592,570,402,552,593,574,406,556,590,575,407,557,588,573,405,555,589,401,569,597,559,399,567,598,560,400,568,599,558,397,565,596,562,398,566,594,563,396,564,595,561,577,578,576,580,581,579,583,584,585,586,587,582,671,669,670,668,294,83,329,316,295,81,327,317,296,82,328,315,297,79,325,312,298,80,326,313,299,78,324,314,74,292,322,335,72,293,323,333,73,291,321,334,77,288,318,331,75,289,319,332,76,290,320,330,301,302,300,304,305,303,307,308,309,310,311,306,678,677,679,676,359,41,341,373,357,39,339,374,358,40,340,372,355,37,337,376,356,38,338,377,354,36,336,375,47,350,379,347,45,348,380,345,46,349,378,346,43,353,382,343,44,351,383,344,42,352,381,342,365,363,364,361,362,360,371,369,366,367,368,370,666,665,667,664,657,658,659,656,648,650,651,649,652,653,654,655,641,640,643,642,644,645,647,646,637,636,639,638,622,620,621,623,614,612,613,615,618,616,617,619,634,633,632,635,626,624,625,627,630,628,629,631,395,393,394,391,392,390,386,384,388,389,387,385,692,694,693,695,85,139,126,116,86,140,127,114,84,138,128,115,88,142,129,119,89,143,130,117,87,141,131,118,137,91,111,124,135,92,112,125,136,90,113,123,133,94,110,120,134,95,108,121,132,93,109,122,105,106,107,104,102,103,96,97,101,99,100,98,700,702,701,703,169,51,165,153,170,52,166,154,168,53,167,155,172,50,164,152,173,48,162,150,171,49,163,151,57,175,144,156,58,176,145,157,59,174,146,158,56,178,147,159,54,179,148,160,55,177,149,161,191,189,190,187,188,186,182,180,184,185,183,181,696,698,697,699,487,26,469,457,488,24,470,458,486,25,468,456,490,29,472,460,491,27,473,461,489,28,471,459,32,485,463,475,30,483,464,476,31,484,462,474,35,481,466,478,33,482,467,479,34,480,465,477,494,492,493,497,495,496,500,498,502,503,501,499,675,673,674,672,198,6,232,221,199,7,233,219,200,8,231,220,201,9,228,217,202,10,229,218,203,11,230,216,4,196,227,238,5,197,225,239,3,195,226,237,1,192,223,234,0,193,224,235,2,194,222,236,204,205,206,207,208,209,210,211,215,213,214,212,680,682,683,681,429,609,411,446,430,610,412,444,431,611,413,445,428,608,410,449,426,606,408,447,427,607,409,448,600,420,452,417,601,421,450,418,602,422,451,419,603,423,455,416,604,424,453,414,605,425,454,415,436,437,435,432,433,434,442,443,440,438,439,441,684,687,685,686 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#a9f62e2491236cd33b6e554b1a4dc1a2938062e1ffa7bd655365fbe4324c4209, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 19:47:32 · history