Equation 677 Database

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Magma 999e7a19d9a9…

magma 999e7a19d9a9
Size
705
Isomorphism class hash
999e7a19d9a9dd61ca8a57409df22db609af23b2cd8431e4d64a760ec3ffb87c
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 20:05:09
Display reorder
704,203,202,201,198,199,200,193,194,192,196,197,195,213,177,29,186,178,187,214,27,179,188,215,28,176,189,212,25,174,190,210,26,175,191,211,24,35,168,184,204,33,169,185,205,34,170,183,206,171,31,180,207,172,32,181,208,173,30,182,209,670,695,699,690,618,620,619,623,621,622,615,616,617,614,612,613,629,636,421,651,637,652,627,422,638,653,628,420,639,650,625,424,640,648,626,425,641,649,624,423,427,642,657,635,428,643,658,633,426,644,659,634,645,430,656,631,646,431,654,632,647,429,655,630,666,696,700,691,593,592,591,588,589,590,598,599,597,594,595,596,606,400,525,410,401,408,607,526,399,409,608,527,396,413,609,524,397,411,610,522,398,412,611,523,516,406,416,604,517,407,414,605,518,405,415,603,402,519,419,600,403,520,417,601,404,521,418,602,663,681,682,671,544,543,545,542,540,541,549,550,551,548,546,547,561,571,358,2,572,1,562,359,570,0,563,357,574,5,560,354,575,3,558,355,573,4,559,356,349,569,8,552,350,567,6,553,348,568,7,554,565,352,11,555,566,353,9,556,564,351,10,557,664,685,687,675,121,120,122,123,124,125,126,127,128,129,130,131,499,513,16,433,514,434,500,17,515,432,498,15,512,436,502,12,510,437,503,13,511,435,501,14,22,504,439,497,23,505,440,495,21,506,438,496,507,18,442,493,508,19,443,494,509,20,441,492,667,697,701,692,286,285,287,284,282,283,276,277,278,279,280,281,292,302,155,270,300,271,293,153,301,272,291,154,305,273,288,151,303,274,289,152,304,275,290,150,146,308,268,298,144,306,269,299,145,307,267,297,311,149,264,294,309,147,265,295,310,148,266,296,668,694,698,689,137,136,135,132,133,134,142,143,141,138,139,140,236,249,221,260,250,258,234,219,251,259,235,220,248,263,239,217,246,261,237,218,247,262,238,216,227,240,255,231,225,241,256,232,226,242,257,233,243,223,254,230,244,224,252,228,245,222,253,229,669,703,702,693,385,384,386,387,388,389,390,391,392,393,394,395,536,365,579,374,363,372,534,580,364,373,535,581,361,377,539,578,362,375,537,576,360,376,538,577,585,371,380,531,586,369,378,532,587,370,379,533,367,584,383,530,368,582,381,528,366,583,382,529,662,686,688,676,315,317,316,313,314,312,323,321,322,319,320,318,326,341,43,58,339,59,324,44,340,57,325,42,337,54,329,46,338,55,327,47,336,56,328,45,41,347,49,332,39,345,50,330,40,346,48,331,343,37,52,335,344,38,53,333,342,36,51,334,665,680,679,673,70,69,71,68,66,67,60,61,62,63,64,65,75,85,163,100,86,101,76,164,84,99,77,162,88,96,74,166,89,97,72,167,87,98,73,165,161,91,106,81,159,92,107,82,160,90,105,83,94,157,102,80,95,158,103,78,93,156,104,79,660,678,677,674,444,446,445,449,447,448,452,450,451,455,453,454,461,469,109,483,470,484,459,110,468,485,460,108,472,482,457,112,473,480,458,113,471,481,456,111,115,475,489,467,116,476,490,465,114,474,491,466,478,118,488,463,479,119,486,464,477,117,487,462,661,684,683,672 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#b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0, M = {61} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 20:05:09 · history