Equation 677 Database

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Magma bfc7320211f0…

magma bfc7320211f0
Size
705
Isomorphism class hash
bfc7320211f025bfb47f866d803f7cce671194f43a945a1353d8eecb6bbdf854
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 19:21:37
Display reorder
704,536,568,553,26,534,24,569,554,535,25,567,552,539,564,29,556,537,565,27,557,538,566,28,555,574,559,531,32,575,560,532,30,573,558,533,31,562,570,530,35,571,563,528,33,572,561,529,34,550,551,549,546,547,548,541,542,543,544,545,540,660,663,661,662,217,209,196,122,218,120,207,197,216,121,208,195,220,205,125,192,221,206,123,193,219,204,124,194,215,202,223,128,213,203,224,126,214,201,222,127,198,211,226,131,212,199,227,129,210,200,225,130,187,188,186,190,191,189,185,183,180,181,182,184,691,689,690,688,420,413,397,591,421,592,411,398,422,593,412,396,423,409,590,400,424,410,588,401,425,408,589,399,419,403,426,597,417,404,427,598,418,402,428,599,406,415,429,596,416,407,430,594,414,405,431,595,392,390,391,395,393,394,387,388,385,386,384,389,671,669,670,668,259,246,234,37,260,38,247,235,258,36,248,236,262,249,40,237,263,250,41,238,261,251,39,239,244,232,257,43,245,233,255,44,243,231,256,42,228,240,253,46,241,229,254,47,242,230,252,45,267,268,269,266,264,265,273,274,271,272,270,275,678,677,679,676,277,317,304,0,278,2,315,305,276,1,316,303,280,313,4,300,281,314,5,301,279,312,3,302,323,310,283,7,321,311,284,8,322,309,282,6,306,319,286,10,320,307,287,11,318,308,285,9,294,295,296,297,298,299,292,293,290,288,289,291,666,665,667,664,658,657,656,659,650,651,648,649,654,655,653,652,642,641,643,640,646,645,647,644,638,636,639,637,621,620,622,623,613,612,614,615,617,616,618,619,632,633,634,635,624,625,626,627,628,629,630,631,585,586,587,584,582,583,576,577,581,579,580,578,692,694,693,695,73,65,100,52,74,53,63,101,72,51,64,99,76,61,48,96,77,62,49,97,75,60,50,98,71,106,79,58,69,107,80,59,70,105,78,57,102,67,82,54,68,103,83,55,66,104,81,56,91,92,90,94,95,93,89,87,84,85,86,88,700,702,701,703,341,327,368,23,339,21,328,366,340,22,329,367,337,326,19,371,338,324,20,369,336,325,18,370,333,363,347,14,334,364,345,12,335,365,346,13,362,332,343,17,330,360,344,15,331,361,342,16,357,358,359,356,354,355,348,349,353,351,352,350,696,698,697,699,514,501,489,115,515,116,502,490,513,114,503,491,510,500,118,488,511,498,119,486,512,499,117,487,492,480,505,113,493,481,506,111,494,482,504,112,483,495,508,109,496,484,509,110,497,485,507,108,519,520,521,518,516,517,525,526,523,524,522,527,675,673,674,672,161,148,135,381,159,382,149,136,160,383,147,137,157,144,380,134,158,145,378,132,156,146,379,133,154,141,167,372,155,142,165,373,153,143,166,374,140,150,163,375,151,138,164,376,152,139,162,377,179,177,178,175,176,174,170,168,172,173,171,169,680,682,683,681,437,470,464,609,435,610,468,462,436,611,469,463,433,473,608,467,434,471,606,465,432,472,607,466,476,459,443,600,474,460,441,601,475,461,442,602,458,479,439,603,477,456,440,604,478,457,438,605,453,454,455,452,450,451,444,445,449,447,448,446,684,687,685,686 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#a08efb2611f2171bf6f734a20baed2f33f3141d650739b05e30e32bcbe11c9bc, 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 19:21:38 · history