Equation 677 Database

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Magma 22664170ff1d…

magma 22664170ff1d
Size
705
Isomorphism class hash
22664170ff1dfa5f9094d04912c264f30f367f4a05901af06cb0164f75794b0f
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 20:08:29
Display reorder
660,616,15,600,612,607,637,16,620,632,627,17,657,640,652,647,597,14,581,592,587,556,12,540,552,547,577,13,560,572,567,21,435,423,432,428,22,457,440,452,447,23,477,461,472,467,496,20,481,492,487,516,18,501,512,507,537,19,521,532,527,686,695,702,700,615,91,617,605,601,635,92,636,625,621,90,655,656,645,641,595,94,596,585,580,555,95,557,545,541,575,93,576,565,561,89,434,436,427,424,87,455,456,445,441,88,475,476,465,460,495,85,497,485,480,515,86,517,505,500,535,84,536,525,520,692,694,699,701,333,127,405,357,381,334,128,406,358,382,126,335,407,359,383,332,130,404,356,380,330,131,402,354,378,331,129,403,355,379,125,324,396,348,372,123,325,397,349,373,124,326,398,350,374,327,121,399,351,375,328,122,400,352,376,329,120,401,353,377,673,670,666,678,417,111,297,345,281,418,112,298,346,279,113,419,299,347,280,416,110,296,344,277,414,108,294,342,278,415,109,295,343,276,117,408,288,336,287,118,409,289,337,285,119,410,290,338,286,411,116,291,339,283,412,114,292,340,284,413,115,293,341,282,667,668,683,663,619,163,610,608,614,639,164,630,628,634,162,659,650,648,654,599,166,590,588,594,559,167,550,548,554,579,165,570,568,574,161,439,431,429,433,159,459,450,448,454,160,479,470,468,474,499,157,490,488,494,519,158,510,508,514,539,156,530,528,534,697,688,689,703,604,78,611,606,613,624,79,631,626,633,80,644,651,646,653,584,81,591,586,593,544,82,551,546,553,564,83,571,566,573,76,438,421,420,422,77,444,451,446,453,75,464,471,466,473,484,72,491,486,493,504,73,511,506,513,524,74,531,526,533,696,687,685,693,618,6,602,603,609,638,7,622,623,629,8,658,642,643,649,598,9,582,583,589,558,10,542,543,549,578,11,562,563,569,4,437,425,426,430,5,458,442,443,449,3,478,462,463,469,498,1,482,483,489,518,0,502,503,509,538,2,522,523,529,690,698,704,691,321,141,182,193,208,322,142,180,194,209,143,323,181,192,207,320,140,185,196,204,318,138,183,197,205,319,139,184,195,206,132,312,188,199,214,133,313,186,200,215,134,314,187,198,213,315,135,191,202,210,316,136,189,203,211,317,137,190,201,212,672,682,665,677,393,34,38,48,65,394,35,36,49,63,33,395,37,50,64,392,30,41,51,61,390,31,39,52,62,391,32,40,53,60,25,384,44,54,71,26,385,42,55,69,24,386,43,56,70,387,28,47,57,67,388,29,45,58,68,389,27,46,59,66,681,661,674,662,262,99,265,369,243,263,100,266,370,244,101,261,264,371,245,258,98,268,368,242,259,96,269,366,240,260,97,267,367,241,105,253,271,360,249,106,254,272,361,250,107,252,270,362,251,256,104,274,363,248,257,102,275,364,246,255,103,273,365,247,684,671,675,679,232,169,147,309,217,233,170,148,310,218,168,231,149,311,216,228,172,146,308,220,229,173,144,306,221,230,171,145,307,219,175,238,153,300,223,176,239,154,301,224,174,237,155,302,222,234,178,152,303,226,235,179,150,304,227,236,177,151,305,225,680,664,676,669 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#ba8e767ab0f178377cc5ca58de8baa4e7db92c571ba3737b1b055d153a9d0c2e, 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 20:08:30 · history