Equation 677 Database

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Magma b621ac3636ca…

magma b621ac3636ca
Size
705
Isomorphism class hash
b621ac3636ca39216e52c1ae45387f938dbf0af8c0ce3da7b7d401d3778f3716
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 15:30:07
Display reorder
660,111,259,180,20,290,112,260,181,18,288,258,182,19,113,289,262,110,183,16,293,263,108,184,17,291,261,109,185,15,292,102,178,11,265,285,103,179,9,266,286,104,177,10,264,287,105,174,14,268,284,106,175,12,269,282,107,176,13,267,283,662,672,664,661,443,58,411,383,419,441,59,412,381,417,57,413,382,442,418,54,439,410,379,415,55,440,408,380,416,56,438,409,378,414,449,402,389,64,425,447,403,387,65,423,448,404,388,63,424,445,405,385,60,421,446,406,386,61,422,444,407,384,62,420,691,687,688,686,140,101,295,572,308,138,99,296,570,306,100,294,571,139,307,97,143,298,568,311,98,141,299,569,309,96,142,297,567,310,146,301,578,92,314,144,302,576,90,312,145,300,577,91,313,149,304,574,95,317,147,305,575,93,315,148,303,573,94,316,670,666,669,668,73,210,500,82,560,74,211,498,83,558,212,499,81,72,559,213,76,496,78,556,214,77,497,79,557,215,75,495,80,555,71,506,88,216,566,69,504,89,217,564,70,505,87,218,565,67,502,84,219,562,68,503,85,220,563,66,501,86,221,561,677,681,682,680,524,224,476,629,548,522,222,474,627,546,223,475,628,523,547,227,520,472,625,544,225,521,473,626,545,226,519,471,624,543,530,482,635,230,554,528,480,633,228,552,529,481,634,229,553,526,478,631,233,550,527,479,632,231,551,525,477,630,232,549,663,667,665,671,395,134,584,431,187,393,132,582,429,188,133,583,430,394,186,137,391,580,427,190,135,392,581,428,191,136,390,579,426,189,401,590,437,129,193,399,588,435,130,194,400,589,436,131,192,397,586,433,128,196,398,587,434,126,197,396,585,432,127,195,699,698,694,695,466,41,28,7,596,467,39,29,8,594,40,27,6,465,595,37,462,24,3,592,38,463,25,4,593,36,464,26,5,591,656,658,657,32,659,651,649,648,30,650,652,654,653,31,655,468,22,0,35,598,469,23,2,33,599,470,21,1,34,597,703,704,701,702,239,116,605,209,455,237,114,603,207,453,115,604,208,238,454,119,235,601,205,451,117,236,602,206,452,118,234,600,204,450,245,611,200,122,461,243,609,198,120,459,244,610,199,121,460,241,607,203,125,457,242,608,201,123,458,240,606,202,124,456,700,696,697,693,371,279,348,163,363,369,280,349,164,364,281,350,162,370,365,278,367,351,166,362,276,368,352,167,360,277,366,353,165,361,377,346,169,270,354,375,347,170,271,355,376,345,168,272,356,373,342,172,273,357,374,343,173,274,358,372,344,171,275,359,673,679,674,684,246,42,488,512,641,247,43,486,510,639,44,487,511,248,640,45,249,484,508,637,46,250,485,509,638,47,251,483,507,636,252,494,518,48,647,253,492,516,49,645,254,493,517,50,646,255,490,514,51,643,256,491,515,52,644,257,489,513,53,642,676,683,675,678,617,154,329,536,335,615,155,327,534,333,153,328,535,616,334,150,613,325,532,331,151,614,326,533,332,152,612,324,531,330,623,320,542,160,341,621,318,540,161,339,622,319,541,159,340,619,323,538,156,337,620,321,539,157,338,618,322,537,158,336,689,685,692,690 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#1c6b3e96bd585e9e8fd52e93592fcd11cb6c83a04227bfcba3bf653b0809cf1c, 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 15:30:10 · history