Equation 677 Database

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Magma e0967523e481…

magma e0967523e481
Size
705
Isomorphism class hash
e0967523e481cd6eab7124602c2f27a55effa84b2945a2d796e39b42e43e1fd1
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 16:51:32
Display reorder
660,621,634,228,632,629,640,654,649,229,652,609,614,601,230,612,541,554,549,231,552,561,574,569,232,572,580,594,589,233,592,448,452,234,442,450,470,476,235,461,473,430,436,236,420,433,516,510,237,502,513,534,529,238,521,532,496,490,239,482,493,697,701,696,692,630,627,198,635,633,650,647,653,199,655,613,607,610,200,615,550,547,553,201,555,570,567,573,202,575,590,587,593,203,595,451,446,196,449,453,474,468,197,471,477,434,428,195,431,437,508,514,192,511,517,527,533,193,530,535,488,494,194,491,497,694,699,702,698,9,346,273,406,382,10,347,383,274,407,381,345,11,275,405,8,342,378,272,402,6,343,379,270,403,7,344,380,271,404,373,337,264,1,397,374,338,265,0,398,372,336,266,2,396,340,376,267,3,400,341,377,268,4,401,339,375,269,5,399,664,666,676,672,300,334,174,370,418,301,335,419,175,371,417,333,302,176,369,303,330,414,177,366,304,331,415,178,367,305,332,416,179,368,409,325,172,306,361,410,326,173,307,362,408,324,171,308,360,328,412,168,309,364,329,413,169,310,365,327,411,170,311,363,677,665,669,678,626,638,252,628,639,646,658,659,253,648,619,618,606,254,608,546,558,559,255,548,566,578,579,256,568,586,598,599,257,588,458,459,258,445,447,478,479,259,467,469,438,439,260,427,429,519,518,261,507,509,539,538,262,526,528,499,498,263,487,489,688,690,685,695,624,631,36,623,620,644,651,641,37,643,600,611,604,38,603,544,551,540,39,543,564,571,560,40,563,584,591,581,41,583,456,457,42,441,440,460,472,43,465,464,421,432,44,425,424,512,501,45,505,504,531,520,46,524,523,492,481,47,485,484,687,691,693,700,636,637,76,625,622,657,656,642,77,645,602,617,616,75,605,556,557,542,72,545,576,577,562,73,565,597,596,582,74,585,454,455,82,443,444,463,475,83,462,466,423,435,81,422,426,515,503,78,500,506,537,522,79,536,525,495,483,80,480,486,704,703,686,689,100,123,323,250,113,101,124,111,321,251,112,125,99,322,249,96,122,109,319,246,97,120,110,320,247,98,121,108,318,248,119,129,314,106,241,117,130,312,107,242,118,131,313,105,240,128,115,317,102,244,126,116,315,103,245,127,114,316,104,243,670,679,661,662,219,284,23,358,33,220,282,34,21,359,35,283,221,22,357,218,287,32,19,354,216,285,30,20,355,217,286,31,18,356,24,279,14,225,349,25,280,12,226,350,26,281,13,227,348,278,27,17,224,352,276,28,15,222,353,277,29,16,223,351,682,673,667,675,186,148,293,161,136,187,149,137,291,159,135,147,188,292,160,189,144,132,289,157,190,145,133,290,158,191,146,134,288,156,142,154,299,184,167,143,155,297,185,165,141,153,298,183,166,150,138,295,180,163,151,139,296,181,164,152,140,294,182,162,671,681,684,683,71,88,211,59,394,69,89,395,212,57,393,87,70,210,58,67,84,390,214,55,68,85,391,215,56,66,86,392,213,54,385,94,209,62,50,386,95,207,60,48,384,93,208,61,49,90,388,205,65,53,91,389,206,63,51,92,387,204,64,52,663,668,680,674 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#41328e14760452489c50b79fcc49c074869181cbfbd0a816da081f28123ef346, M = {60} 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 16:51:33 · history