Equation 677 Database

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Magma f7da16651629…

magma f7da16651629
Size
705
Isomorphism class hash
f7da1665162938ff3aa437a47106b2f21d95b24f69744a4619c762adfe4fc2f9
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 20:44:55
Display reorder
660,600,611,588,315,576,601,612,589,316,577,599,613,587,314,575,596,610,584,318,572,597,608,585,319,573,598,609,586,317,574,606,617,321,594,582,607,618,322,595,583,605,619,320,593,581,616,602,324,590,578,614,603,325,591,579,615,604,323,592,580,687,688,686,685,412,432,401,197,391,410,433,402,195,389,411,431,403,196,390,415,428,400,200,387,413,429,398,198,388,414,430,399,199,386,418,423,203,407,397,416,424,201,408,395,417,422,202,409,396,426,421,206,406,393,427,419,204,404,394,425,420,205,405,392,703,704,701,702,526,545,571,309,548,524,546,569,310,549,525,547,570,308,550,529,544,567,312,551,527,542,568,313,552,528,543,566,311,553,532,536,307,562,554,530,537,305,560,555,531,538,306,561,556,539,535,303,565,557,540,533,304,563,558,541,534,302,564,559,671,672,670,669,213,142,16,190,440,214,143,17,191,441,215,141,15,189,442,216,145,19,193,443,217,146,20,194,444,218,144,18,192,445,211,140,188,22,438,212,138,186,23,439,210,139,187,21,437,136,207,184,25,434,137,208,185,26,435,135,209,183,24,436,679,680,678,677,221,242,264,450,243,219,240,265,451,244,220,241,266,449,245,224,238,263,446,246,222,239,261,447,247,223,237,262,448,248,227,233,456,255,249,225,231,457,256,250,226,232,455,257,251,236,230,452,258,252,234,228,453,259,253,235,229,454,260,254,692,691,690,689,34,285,162,10,488,35,286,163,11,489,33,287,164,9,490,37,288,161,13,491,38,289,159,14,492,36,290,160,12,493,32,283,8,168,486,30,284,6,169,487,31,282,7,170,485,279,28,4,167,482,280,29,5,165,483,281,27,3,166,484,699,700,698,697,84,130,65,45,60,85,131,63,46,61,86,129,64,47,62,83,133,68,48,59,81,134,66,49,57,82,132,67,50,58,75,128,43,71,51,76,126,44,69,52,77,127,42,70,53,124,78,39,74,54,125,79,40,72,55,123,80,41,73,56,663,664,662,661,646,327,635,104,628,644,328,636,102,626,645,326,637,103,627,649,330,634,100,631,647,331,632,101,629,648,329,633,99,630,652,333,110,641,623,650,334,108,642,624,651,332,109,643,625,336,655,106,640,622,337,653,107,638,620,335,654,105,639,621,682,683,684,681,2,522,501,177,294,1,523,502,178,295,0,521,500,179,293,506,519,504,180,291,657,658,656,181,659,505,520,503,182,292,509,514,175,499,297,507,515,176,497,298,508,513,174,498,296,517,512,171,495,300,518,510,172,496,301,516,511,173,494,299,695,696,693,694,474,272,466,156,93,475,270,464,157,94,473,271,465,158,95,470,268,469,155,96,471,269,467,153,97,472,267,468,154,98,480,278,147,461,91,481,276,148,462,92,479,277,149,463,90,274,476,150,460,87,275,477,151,458,88,273,478,152,459,89,667,668,665,666,359,362,344,121,384,360,363,345,122,385,361,364,346,120,383,358,365,347,117,380,356,366,348,118,381,357,367,349,119,382,350,368,112,342,375,351,369,113,343,376,352,370,111,341,374,371,353,115,338,378,372,354,116,339,379,373,355,114,340,377,675,676,673,674 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#d33e4a3e2f8aecd7db8c3ccbf48af948a122b54aec333d772566c797fe9ef74b, 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 20:44:57 · history