Equation 677 Database

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Magma 77d25f4e1580…

magma 77d25f4e1580
Size
705
Isomorphism class hash
77d25f4e1580a414ebd669f30af01c6c2f1ff39b6f635f8d8076beca7e2a1055
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 17:21:15
Display reorder
660,608,622,596,642,47,45,620,609,597,643,46,621,610,598,641,611,43,625,599,638,612,44,623,600,639,42,613,624,601,640,602,38,614,628,633,36,615,626,603,634,37,616,627,604,632,617,41,631,605,636,618,39,629,606,637,619,40,630,607,635,687,688,686,685,428,439,416,395,262,263,440,426,414,393,261,438,427,415,394,424,265,435,412,398,425,266,436,413,396,264,423,437,411,397,407,268,419,430,401,269,417,431,405,399,267,418,429,406,400,422,271,433,410,404,420,272,434,408,402,421,270,432,409,403,703,704,701,702,105,117,591,17,27,28,115,103,592,15,29,116,104,590,16,101,26,113,594,13,102,24,114,595,14,25,100,112,593,12,589,33,96,108,23,34,94,106,587,21,35,95,107,588,22,99,32,111,585,19,97,30,109,586,20,98,31,110,584,18,671,672,670,669,465,72,457,447,243,244,70,466,458,448,245,71,467,456,449,468,246,75,453,450,469,247,73,454,451,248,470,74,455,452,463,241,471,78,445,242,472,76,464,446,240,473,77,462,444,474,237,81,459,441,475,238,79,460,442,476,239,80,461,443,679,680,678,677,253,483,504,494,183,181,484,254,505,492,182,485,252,506,493,249,179,486,503,490,250,180,487,501,491,178,251,488,502,489,510,189,259,481,500,187,260,482,511,498,188,258,480,512,499,255,185,477,509,496,256,186,478,507,497,257,184,479,508,495,692,691,690,689,87,292,202,215,569,567,293,85,203,216,568,291,86,204,214,83,572,295,205,218,84,570,296,206,219,571,82,294,207,217,208,564,93,290,221,565,91,288,209,222,566,92,289,210,220,89,563,286,211,224,90,561,287,212,225,88,562,285,213,223,699,700,698,697,165,177,153,141,126,124,175,163,151,139,125,176,164,152,140,161,129,173,149,137,162,127,174,150,138,128,160,172,148,136,144,121,156,168,132,122,154,166,142,130,123,155,167,143,131,159,120,171,147,135,157,118,169,145,133,158,119,170,146,134,663,664,662,661,338,303,326,314,646,644,304,336,324,312,645,305,337,325,313,334,649,306,322,310,335,647,307,323,311,648,333,308,321,309,332,652,344,301,320,650,342,302,330,318,651,343,300,331,319,340,655,297,328,316,341,653,298,329,317,339,654,299,327,315,682,683,684,681,55,580,61,234,3,4,581,56,62,235,5,579,54,63,233,58,2,583,60,232,656,1,658,657,659,0,57,582,59,236,67,9,53,578,227,10,51,576,68,228,11,52,577,69,226,49,8,574,66,230,50,6,575,64,231,48,7,573,65,229,695,696,693,694,530,542,518,552,191,192,540,528,516,553,190,541,529,517,554,526,194,538,514,551,527,195,539,515,549,193,525,537,513,550,524,197,536,548,558,198,534,546,522,559,196,535,547,523,560,532,200,544,520,557,533,201,545,521,555,531,199,543,519,556,667,668,665,666,380,390,368,356,274,275,391,378,366,354,273,392,379,367,355,376,277,389,364,352,377,278,387,365,353,276,375,388,363,351,359,280,371,381,347,281,369,382,357,345,279,370,383,358,346,374,283,384,362,350,372,284,385,360,348,373,282,386,361,349,675,676,673,674 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#4f5c530836fd0cc12915654d9cb933b30b1ebf0f1cb96882ec953efd42c5ac65, 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 17:21:16 · history