Equation 677 Database

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Magma afb1b0bfded8…

magma afb1b0bfded8
Size
705
Isomorphism class hash
afb1b0bfded877459ff1bd13172fca78c953c8b35d84aeee46dca06a6c6ba6ca
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 16:27:58
Display reorder
660,62,386,243,434,190,60,387,241,435,191,61,385,242,433,192,65,239,382,430,193,383,240,63,431,194,64,384,432,195,238,440,249,392,68,196,441,247,393,66,197,439,248,391,67,198,245,436,388,71,199,69,246,437,389,200,244,438,390,70,201,670,663,665,672,43,302,287,624,516,44,303,288,625,517,42,301,286,623,515,46,290,298,620,512,299,291,47,621,513,45,300,622,514,289,630,293,308,41,522,631,294,309,39,523,629,292,307,40,521,296,626,304,37,518,38,297,627,305,519,295,628,306,36,520,688,685,691,689,86,410,600,564,528,84,411,601,565,529,85,409,599,563,527,89,596,406,560,524,407,597,87,561,525,88,408,562,526,598,570,606,416,92,534,571,607,417,90,535,569,605,415,91,533,602,566,412,95,530,93,603,567,413,531,604,568,414,94,532,667,664,668,669,13,576,470,552,161,14,577,471,553,162,12,575,469,551,160,16,466,572,548,164,573,467,17,549,165,15,574,550,163,468,558,476,582,19,159,559,477,583,20,157,557,475,581,18,158,472,554,578,22,155,23,473,555,579,156,474,556,580,21,154,682,680,679,676,260,636,374,359,30,261,637,375,360,31,259,635,373,358,32,256,370,632,362,33,633,371,257,363,34,258,634,361,35,372,365,380,642,251,28,366,381,643,252,29,364,379,641,250,27,376,368,638,254,24,255,377,369,639,25,378,367,640,253,26,662,671,666,661,80,612,207,540,402,78,613,205,541,400,79,611,206,539,401,83,203,608,536,405,609,204,81,537,403,82,610,538,404,202,546,213,618,75,397,547,211,619,76,398,545,212,617,77,399,209,542,614,74,396,72,210,543,615,394,208,544,616,73,395,696,699,698,693,128,505,144,140,482,126,506,145,141,483,127,504,143,142,481,131,147,501,139,478,502,148,129,137,479,130,503,138,480,146,132,150,511,123,488,659,657,658,124,656,133,149,510,125,487,153,134,507,122,484,120,151,135,508,485,152,136,509,121,486,702,703,704,701,59,458,493,422,272,57,459,494,423,273,58,457,492,421,271,55,489,454,418,268,455,490,56,419,269,54,456,420,270,491,428,499,464,50,263,429,500,465,48,264,427,498,463,49,262,495,424,460,53,266,51,496,425,461,267,497,426,462,52,265,700,695,694,697,109,446,231,588,178,110,447,229,589,179,108,445,230,587,180,112,227,442,584,181,443,228,113,585,182,111,444,586,183,226,594,237,452,115,184,595,235,453,116,185,593,236,451,114,186,233,590,448,118,187,119,234,591,449,188,232,592,450,117,189,678,675,681,684,278,648,350,335,325,279,649,351,336,326,277,647,349,334,327,274,346,644,338,324,645,347,275,339,322,276,646,337,323,348,341,356,654,284,331,342,357,655,285,332,340,355,653,283,333,352,344,650,280,330,281,353,345,651,328,354,343,652,282,329,673,683,677,674,11,171,222,318,106,9,169,220,316,107,10,170,221,317,105,7,225,167,321,102,168,223,8,319,103,6,166,320,104,224,313,217,177,2,97,314,218,175,1,98,315,219,176,0,96,216,312,173,5,100,3,214,310,174,101,215,311,172,4,99,687,686,690,692 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#3233330d12681148716a4d7ca0430e02a433d3f211b7945abf3bfa7e2eafe60e, 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 16:28:00 · history