Equation 677 Database

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Magma 5c29a17aeb2e…

magma 5c29a17aeb2e
Size
705
Isomorphism class hash
5c29a17aeb2e45b4be48df23e499cee5ba08807328571577b1d27e797ee404a0
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 20:04:56
Display reorder
704,511,510,512,513,514,515,508,509,507,504,505,506,477,486,50,501,487,502,478,48,488,503,479,49,489,500,476,53,490,498,474,51,491,499,475,52,56,484,492,468,54,485,493,469,55,483,494,470,480,59,495,471,481,57,496,472,482,58,497,473,669,684,688,691,25,24,26,27,28,29,30,31,32,33,34,35,620,633,298,643,634,644,618,299,635,642,619,297,632,646,623,294,630,647,621,295,631,645,622,296,289,624,641,615,290,625,639,616,288,626,640,617,627,292,637,614,628,293,638,612,629,291,636,613,679,695,701,694,430,429,431,428,426,427,420,421,422,423,424,425,435,445,186,461,446,459,436,187,444,460,437,188,448,457,434,189,449,458,432,190,447,456,433,191,184,451,467,441,185,452,465,442,183,450,466,443,454,180,463,440,455,181,464,438,453,182,462,439,662,671,678,677,4,3,5,2,1,0,9,10,11,8,6,7,307,321,21,331,322,332,308,22,323,330,306,23,320,334,310,20,318,335,311,18,319,333,309,19,12,312,329,305,13,313,327,303,14,314,328,304,315,15,325,301,316,16,326,302,317,17,324,300,667,687,690,686,262,261,263,260,258,259,252,253,254,255,256,257,267,278,338,246,276,247,268,336,277,248,269,337,281,249,266,341,279,250,264,339,280,251,265,340,344,284,244,273,342,282,245,274,343,283,243,275,287,347,240,272,285,345,241,270,286,346,242,271,682,698,700,697,67,66,68,69,70,71,64,65,63,60,61,62,403,119,130,107,117,105,404,131,118,106,402,129,115,103,406,126,116,104,407,127,114,102,405,128,121,110,98,401,122,108,96,399,120,109,97,400,113,124,101,397,111,125,99,398,112,123,100,396,681,696,702,692,78,80,79,83,81,82,75,76,77,74,72,73,212,225,197,236,226,234,210,195,227,235,211,196,224,239,215,193,222,237,213,194,223,238,214,192,203,216,231,207,201,217,232,208,202,218,233,209,219,199,230,206,220,200,228,204,221,198,229,205,660,665,666,664,552,554,553,557,555,556,560,558,559,563,561,562,517,531,41,540,532,541,518,39,533,542,516,40,530,543,520,37,528,544,521,38,529,545,519,36,47,537,546,523,45,538,547,524,46,539,548,522,536,43,549,526,534,44,550,527,535,42,551,525,668,685,689,683,165,167,166,163,164,162,158,156,157,161,159,160,179,134,408,148,132,149,177,409,133,147,178,410,137,144,175,411,135,145,176,412,136,146,174,413,414,140,154,170,415,138,155,168,416,139,153,169,143,417,150,173,141,418,151,171,142,419,152,172,680,703,699,693,372,374,373,377,375,376,380,378,379,383,381,382,389,356,86,370,354,371,387,84,355,369,388,85,359,366,385,89,357,367,386,87,358,368,384,88,92,351,361,395,90,352,362,393,91,353,360,394,350,95,364,391,348,93,365,392,349,94,363,390,663,672,676,674,576,578,577,581,579,580,584,582,583,587,585,586,593,602,657,564,600,565,591,658,601,566,592,659,605,567,589,656,603,568,590,654,604,569,588,655,648,608,570,599,649,606,571,597,650,607,572,598,611,651,573,595,609,652,574,596,610,653,575,594,661,673,675,670 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#b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0, M = {61} 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 20:04:57 · history