Equation 677 Database

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Magma f4de9b546af9…

magma f4de9b546af9
Size
705
Isomorphism class hash
f4de9b546af9025fc852a06dbfe54ce674a5ac331df42aa249f81a4e0c209055
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 20:03:54
Display reorder
660,515,421,103,565,277,101,516,566,278,422,423,514,102,567,279,99,420,518,564,276,418,100,519,562,274,98,419,517,563,275,94,513,412,556,268,92,511,413,557,269,93,512,414,558,270,509,97,415,559,271,510,95,416,560,272,508,96,417,561,273,669,672,667,665,138,174,32,245,589,33,136,246,590,172,173,137,31,244,591,28,177,141,248,588,175,29,139,249,586,30,176,140,247,587,23,144,180,251,580,24,142,178,252,581,22,143,179,250,582,147,26,183,254,583,145,27,181,255,584,146,25,182,253,585,690,688,687,685,457,481,54,289,577,52,458,290,578,482,483,459,53,291,579,57,480,456,288,576,478,55,454,286,574,56,479,455,287,575,49,448,472,280,568,50,449,473,281,569,51,450,474,282,570,451,48,475,283,571,452,46,476,284,572,453,47,477,285,573,664,670,666,668,461,433,187,159,373,188,462,157,374,434,435,460,189,158,375,186,432,464,155,372,430,184,465,156,370,185,431,463,154,371,193,467,424,150,364,194,468,425,148,365,195,466,426,149,366,470,192,427,153,367,471,190,428,151,368,469,191,429,152,369,673,675,682,677,386,601,135,409,389,133,387,410,390,602,603,385,134,411,388,131,600,382,408,392,598,132,383,406,393,130,599,384,407,391,126,377,592,400,395,124,378,593,401,396,125,376,594,402,394,380,129,595,403,398,381,127,596,404,399,379,128,597,405,397,662,661,663,671,485,541,43,521,505,44,486,522,506,542,543,484,45,520,507,42,540,488,524,504,538,40,489,525,502,41,539,487,523,503,34,491,532,527,496,35,492,533,528,497,36,490,534,526,498,494,37,535,530,499,495,38,536,531,500,493,39,537,529,501,694,696,693,697,120,110,80,70,647,81,655,654,652,653,659,657,82,656,658,83,113,121,78,644,111,84,122,79,645,85,112,123,77,646,86,118,108,73,639,87,119,109,71,640,88,117,107,72,638,114,89,104,76,642,115,90,105,74,643,116,91,106,75,641,703,702,701,704,445,553,363,12,622,361,446,648,649,554,555,447,362,651,650,359,552,444,14,623,550,360,442,15,624,358,551,443,13,625,354,436,544,17,620,352,437,545,18,621,353,438,546,16,619,439,357,547,20,616,440,355,548,21,617,441,356,549,19,618,699,700,695,698,333,320,4,306,349,5,331,304,350,321,319,332,3,305,351,1,316,329,309,348,317,0,330,307,346,2,318,328,308,347,10,339,326,312,340,11,337,327,310,341,9,338,325,311,342,335,6,322,315,343,336,7,323,313,344,334,8,324,314,345,681,674,684,676,225,214,160,635,242,161,223,636,243,215,216,224,162,637,241,163,217,221,634,238,218,164,222,632,239,165,219,220,633,240,166,231,212,626,233,167,229,213,627,234,168,230,211,628,232,227,169,208,629,236,228,170,209,630,237,226,171,210,631,235,683,678,679,680,262,301,198,613,67,196,263,614,68,302,303,264,197,615,69,201,300,265,612,66,298,199,266,610,64,200,299,267,611,65,204,260,292,604,58,202,261,293,605,59,203,259,294,606,60,256,207,295,607,61,257,205,296,608,62,258,206,297,609,63,689,686,692,691 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#b88a5e69f4f2e8155017edd6b5c4ba2f90c1abf217fa4fb1e3b057bac30e1168, 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 20:03:55 · history