Equation 677 Database

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Magma 5dc6cd0ce3ff…

magma 5dc6cd0ce3ff
Size
705
Isomorphism class hash
5dc6cd0ce3ff9b3979d35a06d6adaabd12fa07e15fcd00f13b236727dca16f1e
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 20:42:31
Display reorder
704,51,19,35,36,52,20,37,33,53,18,38,34,22,50,31,39,23,48,32,40,49,21,41,30,17,57,26,42,58,15,43,24,59,16,44,25,13,56,29,45,54,14,46,27,55,12,47,28,60,61,62,63,64,65,66,67,71,69,70,68,683,680,682,681,243,543,227,229,244,544,230,225,245,545,228,226,542,242,223,232,540,240,224,233,241,541,231,222,549,249,218,235,250,550,236,216,251,551,234,217,548,248,221,238,246,546,239,219,247,547,237,220,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,465,76,433,450,466,77,451,434,467,75,452,432,72,464,436,453,73,462,437,454,463,74,455,435,82,456,439,448,457,83,449,440,458,81,447,438,78,459,442,444,460,79,445,443,461,80,446,441,476,474,475,479,477,478,471,472,469,470,468,473,669,671,668,670,215,373,182,198,213,374,199,180,214,372,200,181,376,211,185,201,377,212,183,202,210,375,203,184,379,206,188,196,204,380,197,186,205,378,195,187,382,209,191,192,207,383,193,189,208,381,194,190,177,178,179,176,174,175,168,169,173,171,172,170,679,676,678,677,502,10,520,537,503,11,538,521,501,9,539,519,6,498,516,536,7,499,517,534,500,8,535,518,0,493,526,528,494,2,529,527,492,1,530,525,4,496,522,531,497,5,532,523,495,3,533,524,510,511,512,513,514,515,508,509,506,504,505,507,689,690,688,691,620,264,638,610,618,265,611,636,619,266,609,637,267,623,641,606,268,621,639,607,622,269,608,640,270,615,644,601,616,271,602,642,617,272,600,643,273,614,647,604,612,274,605,645,613,275,603,646,635,633,634,631,632,630,626,624,628,629,627,625,692,694,693,695,111,488,93,97,112,486,98,94,113,487,96,95,491,110,92,100,489,108,90,101,109,490,99,91,483,117,84,103,118,484,104,85,119,485,102,86,482,116,87,106,114,480,107,88,115,481,105,89,120,121,122,123,124,125,126,127,131,129,130,128,661,662,660,663,312,148,294,305,313,149,303,295,314,147,304,296,144,315,297,301,145,316,298,302,317,146,300,299,154,318,292,311,319,155,309,293,320,153,310,291,150,321,288,307,322,151,308,289,323,152,306,290,278,276,277,281,279,280,284,282,286,287,285,283,685,686,684,687,327,162,355,363,328,163,364,356,329,164,365,354,165,326,358,362,166,324,359,360,325,167,361,357,160,333,353,369,334,161,370,351,335,159,371,352,156,332,349,368,330,157,366,350,331,158,367,348,336,337,338,339,340,341,342,343,347,345,346,344,698,697,699,696,388,137,414,424,389,135,425,415,387,136,423,416,133,384,417,420,134,385,418,421,386,132,422,419,143,394,412,430,395,141,431,413,393,142,429,411,139,390,408,426,391,140,427,409,392,138,428,410,396,397,398,399,400,401,402,403,407,405,406,404,666,665,667,664,578,262,560,568,576,263,569,558,577,261,567,559,258,581,563,564,259,579,561,565,580,260,566,562,253,584,555,574,582,254,575,556,583,252,573,557,256,587,554,570,585,257,571,552,586,255,572,553,591,592,593,590,588,589,597,598,595,596,594,599,674,673,675,672 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#cce41c1fd55a940f76617a374756c8d0de5f99032cd8fe3feeb0eb2c48843df6, 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 20:42:32 · history