Equation 677 Database

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Magma a0f8ca94bd46…

magma a0f8ca94bd46
Size
705
Isomorphism class hash
a0f8ca94bd467c2969250e4168cf148402205ee1c95ec0e465f3b2d8cb097204
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 19:09:22
Display reorder
660,393,381,369,405,154,394,155,382,370,406,383,156,395,371,407,153,396,384,372,408,151,397,385,373,409,152,398,386,374,410,375,387,399,160,411,388,400,161,376,412,389,401,162,377,413,402,390,159,378,414,403,391,157,379,415,404,392,158,380,416,685,686,688,687,511,497,254,94,224,512,225,495,255,95,496,223,510,253,96,227,507,500,257,93,228,508,498,258,91,226,509,499,256,92,252,492,502,230,100,493,503,231,250,101,494,501,229,251,102,505,491,233,248,99,506,489,234,249,97,504,490,232,247,98,701,702,704,703,66,364,631,616,150,64,148,365,629,614,363,149,65,630,615,146,62,367,627,619,147,63,368,628,617,145,61,366,626,618,622,362,57,141,611,360,55,139,620,612,361,56,140,621,613,60,358,144,625,610,58,359,142,623,608,59,357,143,624,609,670,669,672,671,263,519,21,90,11,264,9,520,22,88,521,10,262,23,89,7,259,522,20,86,8,260,523,18,87,6,261,524,19,85,12,517,269,2,81,518,270,1,13,79,516,268,0,14,80,265,513,5,15,84,266,514,3,16,82,267,515,4,17,83,680,677,679,678,549,537,525,561,280,550,281,538,526,562,539,282,551,527,563,279,552,540,528,564,277,553,541,529,565,278,554,542,530,566,531,543,555,271,567,544,556,272,532,568,545,557,273,533,569,558,546,274,534,570,559,547,275,535,571,560,548,276,536,572,689,690,691,692,123,35,332,593,189,121,187,33,333,591,34,188,122,331,592,192,126,31,335,596,190,124,32,336,594,191,125,30,334,595,338,26,118,195,588,24,119,193,339,589,25,120,194,337,590,117,29,198,341,587,115,27,196,342,585,116,28,197,340,586,697,698,700,699,180,170,655,640,73,178,74,171,653,638,169,75,179,654,639,76,176,173,651,643,77,177,174,652,641,78,175,172,650,642,646,168,186,71,635,166,184,72,644,636,167,185,70,645,637,182,164,67,649,634,183,165,68,647,632,181,163,69,648,633,661,662,664,663,417,455,441,429,210,418,208,453,442,430,454,209,419,443,431,206,420,458,444,432,207,421,456,445,433,205,422,457,446,434,447,461,423,201,435,459,424,199,448,436,460,425,200,449,437,426,464,204,450,438,427,462,202,451,439,428,463,203,452,440,682,681,684,683,41,346,604,49,133,42,134,347,602,50,348,135,43,603,51,136,40,345,607,52,137,38,343,605,53,138,39,344,606,54,600,352,37,131,47,353,36,132,601,48,656,657,130,658,659,354,351,127,599,46,355,349,128,597,44,356,350,129,598,45,693,694,696,695,319,312,305,294,575,320,573,310,306,292,311,574,321,304,293,578,322,308,301,290,576,323,309,302,291,577,324,307,303,289,296,318,325,581,285,316,326,579,297,283,317,327,580,295,284,328,314,584,299,288,329,315,582,300,286,330,313,583,298,287,666,665,668,667,106,213,480,472,241,107,242,211,481,473,212,243,108,482,471,244,105,216,479,475,245,103,214,477,476,246,104,215,478,474,486,219,112,239,470,217,113,240,487,468,218,114,238,488,469,111,222,235,485,466,109,220,236,483,467,110,221,237,484,465,674,673,676,675 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#8cce333a947232ca69e33881346ef6b490f8a5c022184a0ee2c46fc59b5e71a5, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 19:09:23 · history