Equation 677 Database

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Magma 69bb1188d8a9…

magma 69bb1188d8a9
Size
705
Isomorphism class hash
69bb1188d8a9c043a135377ae0be6e8fe9330d24133797225264dda27d38e50e
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 21:19:51
Display reorder
704,444,64,473,486,445,65,487,471,446,63,488,472,447,60,469,489,448,61,470,490,449,62,491,468,450,70,479,484,71,451,485,477,69,452,483,478,66,453,475,480,67,454,481,476,455,68,482,474,462,463,464,465,466,467,460,461,458,456,457,459,700,703,701,702,658,659,656,657,650,651,649,648,654,655,653,652,642,643,640,641,646,647,645,644,638,639,637,636,622,623,620,621,615,614,613,612,619,618,617,616,635,634,632,633,627,626,625,624,630,631,629,628,153,154,155,152,150,151,144,145,149,147,148,146,688,691,689,690,253,276,229,250,254,277,251,230,252,278,249,228,256,279,232,246,257,280,233,247,255,281,248,231,259,282,235,241,283,260,242,236,284,258,240,234,285,262,238,244,286,263,245,239,261,287,243,237,225,226,227,224,222,223,216,217,221,219,220,218,675,672,674,673,422,84,397,418,420,85,419,398,421,86,417,396,425,87,400,414,423,88,401,415,424,89,416,399,428,90,403,409,91,426,410,404,92,427,408,402,93,431,406,412,94,429,413,407,430,95,411,405,393,394,395,392,390,391,384,385,389,387,388,386,682,681,683,680,28,163,50,19,29,164,20,48,27,162,18,49,24,166,53,22,25,167,51,23,26,165,21,52,34,161,56,17,159,35,15,54,160,33,16,55,157,30,59,13,158,31,14,57,32,156,12,58,47,45,46,43,44,42,38,36,40,41,39,37,695,693,692,694,347,435,367,374,345,436,372,368,346,437,373,366,343,434,370,377,344,432,371,375,342,433,376,369,338,441,365,380,442,336,378,363,443,337,379,364,440,341,361,383,438,339,381,362,340,439,382,360,350,348,349,353,351,352,356,354,358,359,357,355,696,698,697,699,520,501,541,563,521,502,561,542,519,503,562,540,516,500,544,559,517,498,545,560,518,499,558,543,526,492,547,554,493,527,552,548,494,525,553,546,495,522,550,557,496,523,555,551,524,497,556,549,537,538,539,536,534,535,528,529,533,531,532,530,686,684,685,687,176,1,203,207,174,0,208,201,175,2,209,202,179,3,199,206,177,4,200,204,178,5,205,198,171,6,194,213,7,172,214,192,8,173,215,193,9,170,197,212,10,168,210,195,169,11,211,196,184,185,183,180,181,182,190,191,188,186,187,189,662,661,663,660,335,272,311,316,333,270,317,309,334,271,315,310,331,275,307,312,332,273,308,313,330,274,314,306,326,267,302,322,268,324,323,300,269,325,321,301,266,329,305,318,264,327,319,303,328,265,320,304,291,292,293,290,288,289,297,298,295,296,294,299,679,676,678,677,134,80,109,129,132,78,130,110,133,79,131,108,137,83,112,128,135,81,113,126,136,82,127,111,140,75,115,120,76,138,121,116,77,139,122,114,74,143,118,123,72,141,124,119,142,73,125,117,107,105,106,103,104,102,98,96,100,101,99,97,666,665,667,664,603,515,581,596,604,513,594,579,605,514,595,580,602,511,577,599,600,512,578,597,601,510,598,576,609,506,587,591,504,610,592,585,505,611,593,586,509,608,583,590,507,606,588,584,607,508,589,582,571,572,570,574,575,573,569,567,564,565,566,568,668,670,671,669 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#e9460cea3e471d03fe1a4dfa5e68e64aa509c8601c2a885c863435b22f6faffe, 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 21:19:52 · history