Equation 677 Database

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Magma a579e4b5bced…

magma a579e4b5bced
Size
705
Isomorphism class hash
a579e4b5bcede566b4333fd0b52d742fe003a6c809fdbbbf330425f0fd99494d
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 21:50:07
Display reorder
660,365,364,363,360,361,362,370,371,369,366,367,368,49,50,48,52,53,51,55,56,54,58,59,57,104,102,103,107,105,106,99,100,101,98,96,97,422,420,421,425,423,424,428,426,427,431,429,430,307,308,306,310,311,309,305,303,304,301,302,300,663,670,664,673,611,610,609,606,607,608,601,602,600,604,605,603,487,488,486,490,491,489,485,483,484,481,482,480,202,203,201,198,199,200,193,194,192,196,197,195,228,229,230,231,232,233,234,235,236,237,238,239,542,540,541,545,543,544,548,546,547,551,549,550,682,687,690,694,444,446,445,449,447,448,452,450,451,455,453,454,119,117,118,115,116,114,110,108,109,113,111,112,390,391,392,393,394,395,388,389,387,384,385,386,325,326,324,328,329,327,331,332,330,334,335,333,269,267,268,265,266,264,275,273,274,271,272,270,662,665,671,675,619,618,620,621,622,623,616,617,615,612,613,614,558,559,560,561,562,563,556,557,555,552,553,554,247,248,246,250,251,249,245,243,244,241,242,240,215,213,214,211,212,210,206,204,205,209,207,208,501,502,503,500,498,499,492,493,494,495,496,497,667,677,680,685,575,574,573,570,571,572,565,566,564,568,569,567,625,626,624,628,629,627,631,632,630,634,635,633,129,130,131,128,126,127,120,121,122,123,124,125,141,142,143,140,138,139,132,133,134,135,136,137,511,512,510,514,515,513,509,507,508,505,506,504,661,672,666,674,377,376,375,372,373,374,382,383,381,378,379,380,440,438,439,443,441,442,435,436,437,434,432,433,262,263,261,258,259,260,253,254,252,256,257,255,42,43,44,45,46,47,40,41,39,36,37,38,319,320,318,322,323,321,317,315,316,313,314,312,691,696,697,700,69,71,70,67,68,66,62,60,61,65,63,64,149,147,148,145,146,144,155,153,154,151,152,150,189,190,191,188,186,187,180,181,182,183,184,185,166,167,165,162,163,164,157,158,156,160,161,159,175,176,174,178,179,177,173,171,172,169,170,168,699,704,702,703,466,465,467,464,462,463,456,457,458,459,460,461,32,30,31,35,33,34,27,28,29,26,24,25,583,584,582,586,587,585,581,579,580,577,578,576,645,646,647,644,642,643,636,637,638,639,640,641,522,523,524,525,526,527,520,521,519,516,517,518,692,695,698,701,417,419,418,415,416,414,410,408,409,413,411,412,93,94,95,92,90,91,84,85,86,87,88,89,21,22,23,20,18,19,12,13,14,15,16,17,350,348,349,353,351,352,356,354,355,359,357,358,292,293,291,288,289,290,298,299,297,294,295,296,669,678,679,684,595,594,596,597,598,599,592,593,591,588,589,590,538,539,537,534,535,536,529,530,528,532,533,531,216,217,218,219,220,221,222,223,224,225,226,227,479,477,478,475,476,474,470,468,469,473,471,472,648,649,650,651,652,653,654,655,656,657,658,659,668,676,681,686,4,3,5,2,1,0,9,10,11,8,6,7,336,337,338,339,340,341,342,343,344,345,346,347,396,397,398,399,400,401,402,403,404,405,406,407,278,276,277,281,279,280,284,282,283,287,285,286,83,81,82,79,80,78,74,72,73,77,75,76,683,688,689,693 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {63} 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 21:50:08 · history