Equation 677 Database

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Magma 6dc8d88abbe3…

magma 6dc8d88abbe3
Size
705
Isomorphism class hash
6dc8d88abbe39de9a2126aed5828e73cf9254ce774d62b50dacdcaab4e8ac20d
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 19:42:26
Display reorder
660,522,601,177,207,453,520,178,208,451,599,521,600,179,209,452,597,518,176,206,449,598,519,174,204,450,596,517,175,205,448,168,528,607,213,459,169,526,605,214,457,170,527,606,215,458,524,171,603,212,455,525,172,604,210,456,523,173,602,211,454,686,677,680,687,346,398,380,299,280,347,378,297,281,396,345,397,379,298,279,394,349,376,295,276,395,350,377,296,277,393,348,375,294,278,371,352,404,290,286,369,353,402,288,287,370,351,403,289,285,355,374,400,293,282,356,372,401,291,283,354,373,399,292,284,668,663,671,662,386,565,133,498,185,384,134,496,183,563,385,564,132,497,184,561,382,136,494,181,562,383,137,495,182,560,381,135,493,180,131,392,571,504,191,129,390,569,502,189,130,391,570,503,190,388,127,567,500,187,389,128,568,501,188,387,126,566,499,186,679,674,673,684,153,491,74,26,465,154,72,24,463,489,155,490,73,25,464,487,152,77,29,461,488,150,75,27,462,486,151,76,28,460,69,653,658,652,656,70,637,642,636,640,71,645,650,644,648,620,68,623,624,625,630,66,634,629,632,344,67,492,343,466,704,699,703,701,217,314,34,577,228,218,35,575,229,312,216,313,33,576,230,317,220,30,573,231,315,221,31,574,232,316,219,32,572,233,40,223,320,583,234,41,224,318,581,235,39,222,319,582,236,226,36,323,579,237,227,37,321,580,238,225,38,322,578,239,693,689,690,694,138,422,65,85,479,139,63,86,477,420,140,421,64,84,478,418,141,61,88,475,419,142,62,89,476,417,143,60,87,474,56,144,428,83,485,54,145,426,81,483,55,146,427,82,484,147,59,424,79,481,148,57,425,80,482,149,58,423,78,480,665,666,670,664,261,248,330,22,267,262,331,23,268,246,263,247,332,21,269,251,260,333,18,266,249,258,334,19,264,250,259,335,20,265,328,252,243,13,273,329,253,244,14,274,327,254,245,12,275,255,324,242,16,272,256,325,240,17,270,257,326,241,15,271,695,691,696,692,115,410,192,534,613,116,193,532,611,408,114,409,194,533,612,406,118,195,530,609,407,119,196,531,610,405,117,197,529,608,198,121,416,540,619,199,122,414,538,617,200,120,415,539,618,124,201,412,536,615,125,202,413,537,616,123,203,411,535,614,681,688,678,675,471,555,92,340,446,472,90,341,444,553,473,554,91,342,445,558,470,95,339,442,556,468,93,337,443,557,469,94,338,441,98,657,659,654,655,96,641,643,638,639,97,649,651,646,647,626,101,627,621,622,633,99,635,628,631,467,100,559,336,447,698,697,700,702,589,546,359,308,510,587,357,306,508,544,588,545,358,307,509,542,585,362,311,506,543,586,360,309,507,541,584,361,310,505,365,595,552,303,516,363,593,550,304,514,364,594,551,305,515,591,368,548,302,512,592,366,549,300,513,590,367,547,301,511,661,667,672,669,46,434,105,163,10,47,106,164,11,432,45,433,107,162,9,430,42,104,166,6,431,43,102,167,7,429,44,103,165,8,111,52,440,161,0,112,53,438,159,2,113,51,439,160,1,48,110,436,157,4,49,108,437,158,5,50,109,435,156,3,685,683,682,676 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#a3dbb2a8d5932ce23601e140d077e70c3bff24b108fb14183b80120946e543a6, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 19:42:26 · history