Equation 677 Database

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Magma d24bc251c28c…

magma d24bc251c28c
Size
705
Isomorphism class hash
d24bc251c28ca2a42b10c1809a5c6dcb493da31c6709c46b6cd8d033eb8910ce
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 18:07:49
Display reorder
704,140,84,108,127,138,85,128,109,139,86,126,110,143,87,111,130,141,88,112,131,142,89,129,113,90,135,114,125,91,136,123,115,92,137,124,116,93,134,117,121,94,132,122,118,95,133,120,119,97,98,96,100,101,99,103,104,105,106,107,102,683,680,682,681,545,3,522,531,543,4,532,523,544,5,533,524,541,2,525,530,542,1,526,528,540,0,529,527,9,551,520,537,10,549,538,521,11,550,539,519,8,547,516,536,6,548,534,517,7,546,535,518,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,374,32,404,411,372,30,412,402,373,31,413,403,377,35,407,410,375,33,405,408,376,34,409,406,27,380,399,417,28,378,418,400,29,379,419,401,26,383,398,416,24,381,414,396,25,382,415,397,390,391,392,393,394,395,388,389,386,384,385,387,669,671,668,670,306,155,277,296,307,153,294,278,308,154,295,276,309,151,280,299,310,152,281,297,311,150,298,279,146,304,283,291,144,305,292,284,145,303,293,282,149,300,286,290,147,301,288,287,148,302,289,285,317,315,316,313,314,312,323,321,318,319,320,322,679,676,678,677,493,14,478,482,494,12,480,479,492,13,481,477,496,17,474,485,497,15,475,483,495,16,484,476,20,499,469,488,18,500,486,470,19,498,487,468,23,502,472,491,21,503,489,473,22,501,490,471,512,510,511,515,513,514,507,508,505,506,504,509,689,690,688,691,623,72,638,610,621,73,611,636,622,74,609,637,619,75,641,606,620,76,639,607,618,77,608,640,78,614,644,601,79,612,602,642,80,613,600,643,81,617,647,604,82,615,605,645,83,616,603,646,625,626,624,628,629,627,631,632,633,634,635,630,692,694,693,695,441,44,456,431,442,42,429,457,443,43,430,458,440,47,459,427,438,45,460,428,439,46,426,461,39,432,462,422,40,433,420,463,41,434,421,464,38,435,465,425,36,436,423,466,37,437,424,467,446,444,445,449,447,448,452,450,454,455,453,451,661,662,660,663,216,178,202,206,217,179,204,203,218,177,205,201,219,174,198,209,220,175,199,207,221,176,208,200,169,222,193,212,170,223,210,194,168,224,211,192,172,225,196,215,173,226,213,197,171,227,214,195,189,190,191,188,186,187,180,181,185,183,184,182,685,686,684,687,238,56,254,271,239,54,272,252,237,55,270,253,234,59,257,274,235,57,255,275,236,58,273,256,51,229,260,269,52,230,267,258,53,228,268,259,50,232,263,265,48,233,266,261,49,231,264,262,240,241,242,243,244,245,246,247,251,249,250,248,698,697,699,696,336,157,366,325,337,158,326,367,338,156,324,368,339,160,369,328,340,161,370,329,341,159,327,371,163,342,364,331,164,343,332,365,162,344,330,363,166,345,360,334,167,346,335,361,165,347,333,362,356,354,355,359,357,358,351,352,349,350,348,353,666,665,667,664,582,70,552,572,583,71,570,553,584,69,571,554,585,66,555,575,586,67,556,573,587,68,574,557,61,580,558,567,62,581,568,559,60,579,569,560,64,576,561,566,65,577,564,562,63,578,565,563,591,592,593,590,588,589,597,598,595,596,594,599,674,673,675,672 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#65891b0f2ef20500afb660f1d25606412fdc1bf33a195bdba8e3c07ff4e9e9d9, 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 18:07:50 · history