Equation 677 Database

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Magma db78187fec6c…

magma db78187fec6c
Size
705
Isomorphism class hash
db78187fec6c55432872add3950885f4e997f5f4bb7c1a8d7ed4c6149005a90f
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 15:10:28
Display reorder
660,289,5,209,543,423,210,290,544,424,3,211,4,291,542,422,288,208,0,546,426,286,206,2,547,427,287,207,1,545,425,200,11,541,280,421,201,9,539,281,419,202,10,540,282,420,7,203,537,283,417,8,204,538,284,418,285,6,205,536,416,662,666,661,670,222,387,320,483,224,321,223,484,225,388,322,386,221,482,226,218,323,390,486,227,219,324,391,487,228,220,325,389,485,229,326,385,481,213,230,327,383,479,214,231,328,384,480,212,232,381,329,477,216,233,382,330,478,217,234,215,380,331,476,235,686,690,685,688,250,555,50,531,623,48,248,532,624,556,49,554,249,530,622,253,53,558,534,626,251,51,559,535,627,252,52,557,533,625,56,553,529,256,621,54,551,527,254,619,55,552,528,255,620,549,59,525,259,617,550,57,526,257,618,258,548,58,524,616,671,667,672,669,122,40,30,471,339,31,123,472,340,41,32,39,124,470,338,125,33,36,474,342,126,34,37,475,343,127,35,38,473,341,28,46,469,120,337,29,47,467,121,335,27,45,468,119,336,42,24,465,116,333,43,25,466,117,334,118,44,26,464,332,673,679,674,677,447,507,138,435,459,139,448,436,460,508,137,506,446,434,458,450,134,510,438,462,451,135,511,439,463,449,136,509,437,461,129,505,433,445,457,130,503,431,443,455,128,504,432,444,456,501,132,429,441,453,502,133,430,442,454,440,500,131,428,452,668,664,665,663,244,575,70,102,495,71,242,103,496,576,69,574,243,104,494,247,66,578,105,498,245,67,579,106,499,246,68,577,107,497,61,573,100,239,493,62,571,101,240,491,60,572,99,241,492,569,64,96,238,489,570,65,97,236,490,237,568,63,98,488,697,693,695,696,567,635,92,108,272,90,647,646,645,644,91,634,566,115,279,652,95,654,653,655,656,93,658,657,659,649,94,650,648,651,87,629,114,561,278,88,630,112,562,276,89,628,113,560,277,632,86,110,564,274,633,84,111,565,275,563,631,85,109,273,701,702,704,703,293,301,140,351,599,141,636,352,600,637,142,300,292,350,598,641,143,640,354,602,643,144,642,355,603,638,145,639,353,601,146,307,349,296,597,147,305,347,294,595,148,306,348,295,596,303,149,345,299,593,304,150,346,297,594,298,302,151,344,592,700,699,698,694,404,519,23,375,587,21,405,376,588,520,22,518,406,374,586,407,19,522,378,590,408,20,523,379,591,409,18,521,377,589,14,517,373,410,585,12,515,371,411,583,13,516,372,412,584,513,17,369,413,581,514,15,370,414,582,415,512,16,368,580,682,678,683,676,611,363,177,198,308,178,612,199,309,364,176,362,610,197,310,614,180,366,194,311,615,181,367,195,312,613,179,365,196,313,183,361,189,609,314,184,359,190,607,315,182,360,188,608,316,357,186,192,605,317,358,187,193,606,318,604,356,185,191,319,675,684,681,680,399,165,271,79,157,269,400,80,155,166,270,164,398,78,156,402,267,168,82,153,403,268,169,83,154,401,266,167,81,152,262,171,77,397,163,260,172,75,395,161,261,170,76,396,162,174,265,73,393,159,175,263,74,394,160,392,173,264,72,158,689,687,692,691 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#06e28404eb43925716bfc8e4d73e8cc7ccb918742e903c176b52de636b48f456, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 15:10:29 · history