Equation 677 Database

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Magma 7d02b7d5a8fe…

magma 7d02b7d5a8fe
Size
705
Isomorphism class hash
7d02b7d5a8fe607cf9bce4c8f743d1a69f4d143454574e1588b55a5c303b6dc4
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 16:41:28
Display reorder
660,586,619,373,599,572,573,617,584,371,600,618,574,585,372,601,575,589,615,369,598,587,576,616,370,596,588,577,614,368,597,592,610,379,578,605,590,608,377,579,606,591,609,378,580,607,613,595,375,581,604,611,593,376,582,602,612,594,374,583,603,687,688,686,685,299,279,412,72,285,286,280,297,410,70,281,287,298,411,71,288,302,282,415,68,300,289,283,413,69,301,290,284,414,67,305,277,407,291,63,303,278,408,292,61,304,276,409,293,62,273,308,406,294,66,274,306,404,295,64,275,307,405,296,65,703,704,701,702,48,129,367,568,135,136,130,46,365,566,131,137,47,366,567,134,44,128,363,571,45,132,126,364,569,43,133,127,362,570,39,120,358,141,563,37,121,356,142,564,38,122,357,143,565,123,42,361,140,562,124,40,359,138,560,125,41,360,139,561,671,672,670,669,430,150,317,36,422,423,151,428,315,34,152,424,429,316,35,425,433,153,320,32,431,426,154,318,33,432,427,155,319,31,436,148,312,420,27,434,149,313,421,25,435,147,314,419,26,144,439,311,416,30,145,437,309,417,28,146,438,310,418,29,679,680,678,677,481,462,156,443,473,474,463,479,157,444,461,475,480,158,445,472,477,458,159,442,478,470,459,160,440,476,471,460,161,441,487,453,162,464,449,485,454,163,465,450,486,452,164,466,451,456,483,165,467,448,457,484,166,468,446,455,482,167,469,447,692,691,690,689,243,544,336,174,102,100,542,244,337,175,543,101,245,338,176,98,246,547,335,177,247,99,545,333,178,248,97,546,334,179,241,539,342,108,172,242,540,343,106,173,240,541,344,107,171,538,237,341,104,168,536,238,339,105,169,537,239,340,103,170,699,700,698,697,96,20,2,55,84,87,21,88,3,56,19,81,91,0,57,93,82,23,5,58,86,94,24,6,59,79,89,22,4,60,78,18,8,90,53,76,16,9,92,54,77,17,7,95,52,14,74,11,85,49,15,75,12,80,50,13,73,10,83,51,663,664,662,661,646,626,258,386,632,633,627,644,259,387,628,634,645,260,388,635,649,629,257,389,647,636,630,255,390,648,637,631,256,391,652,624,249,638,384,650,625,250,639,385,651,623,251,640,383,620,655,252,641,380,621,653,253,642,381,622,654,254,643,382,682,683,684,681,351,193,549,118,187,188,194,352,550,119,192,186,353,548,117,190,354,1,552,109,658,656,657,553,659,355,189,191,551,116,349,199,555,185,112,350,200,556,183,110,348,198,554,184,111,195,345,558,181,115,196,346,559,182,113,197,347,557,180,114,695,696,693,694,503,529,329,521,497,498,527,504,327,522,528,499,505,328,523,496,502,525,332,520,500,494,526,330,518,501,495,524,331,519,509,535,324,488,512,510,533,325,489,513,511,534,326,490,514,531,508,323,491,515,532,506,321,492,516,530,507,322,493,517,667,668,665,666,209,225,272,218,398,399,226,207,270,216,227,400,208,271,217,401,212,228,268,214,210,402,229,269,215,211,403,230,267,213,204,231,263,396,224,205,232,261,397,222,206,233,262,395,223,234,203,266,392,220,235,201,264,393,221,236,202,265,394,219,675,676,673,674 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#3a1e3dea02005faeb7a32ea89e0ebcd7060d0e295c5a20add7fb441719113d75, 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 16:41:29 · history