Equation 677 Database

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Magma 0a9af7e29b8e…

magma 0a9af7e29b8e
Size
705
Isomorphism class hash
0a9af7e29b8ed2282ea8ef05860eee2e4e836464a34d9659493b8da87dfa18be
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 21:54:50
Display reorder
660,341,321,356,160,337,322,161,339,354,338,323,159,340,355,336,344,163,324,352,333,342,164,325,353,334,343,162,326,351,335,319,347,362,166,328,320,345,360,167,329,318,346,361,165,327,350,315,358,169,331,348,316,359,170,332,349,317,357,168,330,685,686,688,687,221,419,236,98,217,417,96,219,234,218,418,97,220,235,216,224,94,422,232,213,222,95,420,233,214,223,93,421,231,215,414,227,242,89,208,415,225,240,87,209,416,226,241,88,207,230,413,238,92,211,228,411,239,90,212,229,412,237,91,210,701,702,704,703,614,582,616,303,596,580,304,615,617,597,581,305,613,618,595,610,306,585,619,592,611,307,583,620,593,612,308,584,621,594,588,605,622,309,602,586,606,623,310,603,587,604,624,311,601,608,591,625,312,598,609,589,626,313,599,607,590,627,314,600,670,669,672,671,31,253,431,141,109,254,142,32,429,110,252,143,30,430,108,27,144,249,434,105,28,145,250,432,106,29,146,251,433,107,244,37,426,139,100,245,38,427,140,101,243,36,428,138,99,33,247,425,135,103,34,248,423,136,104,35,246,424,137,102,680,677,679,678,118,458,441,147,255,456,148,119,442,256,457,149,117,443,257,121,150,454,444,258,122,151,455,445,259,120,152,453,446,260,449,116,439,153,261,447,114,440,154,262,448,115,438,155,263,112,452,435,156,264,113,450,436,157,265,111,451,437,158,266,689,690,691,692,535,507,505,279,520,508,280,536,506,521,509,281,534,504,519,531,282,510,501,523,532,283,511,502,524,533,284,512,503,522,513,541,496,285,526,514,542,497,286,527,515,540,495,287,525,537,516,499,288,529,538,517,500,289,530,539,518,498,290,528,697,698,700,699,636,4,651,22,58,5,23,634,649,59,3,21,635,650,57,639,18,1,647,61,637,19,0,648,62,638,20,2,646,60,10,631,642,13,56,11,632,640,14,54,9,633,641,12,55,630,6,645,16,52,628,7,643,17,53,629,8,644,15,51,661,662,664,663,385,181,387,185,369,182,183,386,388,370,180,184,384,389,371,381,188,177,390,372,382,186,178,391,373,383,187,179,392,374,172,376,393,191,367,173,377,394,189,368,171,375,395,190,366,379,175,396,194,363,380,176,397,192,364,378,174,398,193,365,682,681,684,683,564,550,579,295,554,551,296,565,577,552,549,294,566,578,553,567,291,546,575,557,568,292,547,576,555,569,293,548,574,556,657,658,659,301,656,562,563,570,302,558,652,653,654,300,655,25,544,573,297,561,26,545,571,298,559,24,543,572,299,560,693,694,696,695,474,130,483,267,466,131,268,475,484,467,129,269,476,485,465,473,270,133,486,469,471,271,134,487,470,472,272,132,488,468,128,480,489,273,464,126,481,490,274,462,127,482,491,275,463,479,124,492,276,460,477,125,493,277,461,478,123,494,278,459,666,665,668,667,78,202,45,402,64,203,403,79,46,65,201,404,80,47,63,77,401,205,48,67,75,399,206,49,68,76,400,204,50,66,200,84,43,408,70,198,85,44,409,71,199,86,42,410,69,83,196,39,407,73,81,197,40,405,74,82,195,41,406,72,674,673,676,675 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#fbd23cd98406f165f23d6b41307d902a92b7e2e110ccd89116da4983a4804a48, 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 21:54:50 · history