Equation 677 Database

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Magma ec8324cf52c7…

magma ec8324cf52c7
Size
705
Isomorphism class hash
ec8324cf52c754f200f07951390639b69065efb09d973bc51483ab6b96af21e0
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 15:09:12
Display reorder
660,179,338,190,153,159,177,336,191,154,160,178,337,189,155,161,175,341,186,152,158,339,176,187,150,156,174,340,188,151,157,170,344,181,144,165,168,342,182,145,166,169,343,180,146,167,347,173,184,147,164,345,171,185,148,162,346,172,183,149,163,685,686,688,687,286,2,416,261,267,287,1,414,262,268,285,0,415,263,269,282,5,419,260,266,3,283,417,258,264,284,4,418,259,265,277,8,411,252,273,278,6,412,253,274,276,7,413,254,275,11,280,410,255,272,9,281,408,256,270,10,279,409,257,271,701,702,704,703,574,331,578,599,563,575,332,576,597,561,573,330,577,598,562,570,334,581,595,559,335,571,579,596,560,572,333,580,594,558,565,329,584,590,554,566,327,582,588,552,564,328,583,589,553,325,568,587,593,557,326,569,585,591,555,324,567,586,592,556,670,669,672,671,295,90,428,434,454,296,91,426,432,455,294,92,427,433,453,298,93,431,437,450,94,299,429,435,451,297,95,430,436,452,293,88,423,440,445,291,89,424,438,446,292,87,425,439,444,84,289,422,443,448,85,290,420,441,449,86,288,421,442,447,680,677,679,678,53,463,307,98,117,51,464,308,96,118,52,462,306,97,119,49,466,310,101,116,467,50,311,99,114,48,465,309,100,115,59,461,305,104,108,57,459,303,102,109,58,460,304,103,110,457,55,301,107,111,458,56,302,105,112,456,54,300,106,113,689,690,691,692,509,62,138,25,498,507,60,139,26,499,508,61,140,24,500,505,65,141,28,501,63,506,142,29,502,504,64,143,27,503,515,68,136,31,496,513,66,137,32,497,514,67,135,30,495,71,511,132,34,492,69,512,133,35,493,70,510,134,33,494,697,698,700,699,626,47,647,608,612,624,45,645,606,613,625,46,646,607,614,629,43,643,611,615,44,627,644,609,616,628,42,642,610,617,632,38,638,603,618,630,36,636,604,619,631,37,637,605,620,41,635,641,602,621,39,633,639,600,622,40,634,640,601,623,661,662,664,663,377,195,387,357,365,375,196,388,358,363,376,197,389,359,364,373,194,386,356,361,192,374,384,354,362,372,193,385,355,360,383,201,393,348,371,381,202,394,349,369,382,203,395,350,370,200,379,392,351,367,198,380,390,352,368,199,378,391,353,366,682,681,684,683,543,82,522,528,539,544,83,523,529,537,545,81,524,530,538,546,78,521,527,542,79,547,519,525,540,548,80,520,526,541,655,73,653,652,654,659,74,657,656,658,650,72,648,649,651,76,549,516,533,536,77,550,517,531,534,75,551,518,532,535,693,694,696,695,476,320,482,125,13,474,318,480,123,14,475,319,481,124,12,479,323,485,121,16,321,477,483,122,17,478,322,484,120,15,471,315,488,131,19,472,316,486,129,20,473,317,487,130,18,314,470,491,127,22,312,468,489,128,23,313,469,490,126,21,666,665,668,667,204,397,216,228,242,205,398,217,229,240,206,396,218,230,241,207,400,219,231,245,401,208,220,232,243,209,399,221,233,244,210,403,222,234,248,211,404,223,235,246,212,402,224,236,247,406,213,225,237,251,407,214,226,238,249,405,215,227,239,250,674,673,676,675 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#05c0aaa7a3560fa146ae1951a40d178d675f2688aa4f7579703e2b967da3180b, 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 15:09:13 · history