Equation 677 Database

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Magma 610fbf763d21…

magma 610fbf763d21
Size
705
Isomorphism class hash
610fbf763d210e29c8810770251e5e11ebe489fb8009d2a33e136fe7d4713d54
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 20:46:44
Display reorder
660,187,491,485,486,488,188,511,505,506,508,186,531,525,526,528,190,471,465,466,468,191,433,428,430,432,189,451,445,446,448,185,605,611,606,608,183,625,631,626,628,184,645,651,646,648,585,181,591,586,588,545,182,551,546,548,565,180,571,566,568,686,700,690,689,139,495,493,489,490,140,515,513,509,510,138,535,533,529,530,142,475,473,469,470,143,439,438,437,424,141,455,453,449,450,137,613,615,609,610,135,633,635,629,630,136,653,655,649,650,593,133,595,589,590,553,134,555,549,550,573,132,575,569,570,687,685,691,688,158,399,36,74,291,156,400,37,72,292,157,401,38,73,293,161,398,39,77,290,159,396,40,75,288,160,397,41,76,289,164,42,405,80,297,162,43,406,78,298,163,44,407,79,299,45,167,404,83,296,46,165,402,81,294,47,166,403,82,295,663,672,668,678,235,327,320,274,277,236,328,318,275,278,234,329,319,273,276,238,326,323,270,280,239,324,321,271,281,237,325,322,272,279,233,315,333,265,283,231,316,334,266,284,232,317,335,264,282,314,229,332,268,286,312,230,330,269,287,313,228,331,267,285,662,674,661,665,125,492,496,480,494,123,512,516,500,514,124,532,536,521,534,121,472,476,461,474,122,425,427,423,426,120,452,456,440,454,131,616,612,600,614,129,636,632,620,634,130,656,652,641,654,596,127,592,581,594,556,128,552,540,554,576,126,572,561,574,701,702,699,703,258,497,498,499,487,259,517,518,519,507,260,538,537,539,527,261,478,477,479,467,262,420,421,422,431,263,458,457,459,447,256,617,618,619,607,257,638,637,639,627,255,658,657,659,647,597,252,598,599,587,558,253,557,559,547,577,254,578,579,567,695,698,694,697,246,482,481,483,484,247,502,501,503,504,248,522,520,523,524,249,462,460,463,464,250,435,434,436,429,251,442,441,443,444,244,601,602,603,604,245,621,622,623,624,243,640,642,643,644,580,240,582,583,584,541,241,542,543,544,560,242,562,563,564,693,704,696,692,87,22,51,375,108,88,23,52,376,109,89,21,53,377,110,86,18,50,374,111,84,19,48,372,112,85,20,49,373,113,93,57,13,381,114,94,58,14,382,115,95,59,12,383,116,56,92,16,380,117,54,90,17,378,118,55,91,15,379,119,680,675,669,679,71,8,196,223,351,69,6,197,224,352,70,7,195,222,353,67,11,192,226,350,68,9,193,227,348,66,10,194,225,349,62,202,3,221,357,60,203,4,219,358,61,201,5,220,359,198,65,2,217,356,199,63,1,218,354,200,64,0,216,355,670,681,684,666,32,363,387,145,176,30,364,388,146,174,31,365,389,144,175,35,362,386,148,179,33,360,384,149,177,34,361,385,147,178,27,393,369,151,171,28,394,370,152,172,29,395,371,150,173,392,26,368,154,170,390,24,366,155,168,391,25,367,153,169,683,673,677,671,214,339,411,106,303,215,340,412,107,304,213,341,413,105,305,210,338,410,102,302,211,336,408,103,300,212,337,409,104,301,205,417,345,97,309,206,418,346,98,310,204,419,347,96,311,416,208,344,100,308,414,209,342,101,306,415,207,343,99,307,664,676,682,667 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#d3adc358e0fc62ec693454af0a9d8486ee65796d63279744faf9965dafec0a65, 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 20:46:45 · history