Equation 677 Database

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Magma 1f52342aaf52…

magma 1f52342aaf52
Size
705
Isomorphism class hash
1f52342aaf520b83589f0e24516db8a725c98614043e0ed3c680ceae34b50e16
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 20:01:53
Display reorder
704,593,592,591,588,589,590,598,599,597,594,595,596,610,611,609,606,607,608,601,602,600,604,605,603,337,338,336,340,341,339,343,344,342,346,347,345,74,72,73,77,75,76,80,78,79,83,81,82,114,115,116,117,118,119,112,113,111,108,109,110,674,697,693,702,533,532,531,528,529,530,538,539,537,534,535,536,549,550,551,548,546,547,540,541,542,543,544,545,512,510,511,515,513,514,507,508,509,506,504,505,523,524,522,526,527,525,521,519,520,517,518,516,487,488,486,490,491,489,485,483,484,481,482,480,673,695,692,700,356,355,354,358,359,357,353,351,352,349,350,348,362,360,361,365,363,364,368,366,367,371,369,370,374,372,373,377,375,376,380,378,379,383,381,382,393,394,395,392,390,391,384,385,386,387,388,389,0,2,1,4,5,3,7,8,6,10,11,9,664,666,670,683,648,650,649,653,651,652,656,654,655,659,657,658,314,312,313,317,315,316,320,318,319,323,321,322,324,325,326,327,328,329,330,331,332,333,334,335,155,153,154,151,152,150,146,144,145,149,147,148,99,100,101,98,96,97,105,106,107,104,102,103,665,681,675,687,54,56,55,59,57,58,51,52,53,50,48,49,295,296,294,298,299,297,293,291,292,289,290,288,307,308,306,310,311,309,305,303,304,301,302,300,163,164,162,166,167,165,161,159,160,157,158,156,33,34,35,32,30,31,24,25,26,27,28,29,680,694,690,701,431,430,429,426,427,428,421,422,420,424,425,423,440,438,439,443,441,442,435,436,437,434,432,433,403,404,402,406,407,405,401,399,400,397,398,396,417,418,419,416,414,415,408,409,410,411,412,413,41,39,40,37,38,36,47,45,46,43,44,42,676,698,689,703,552,554,553,557,555,556,560,558,559,563,561,562,568,569,567,564,565,566,574,575,573,570,571,572,19,20,18,22,23,21,17,15,16,13,14,12,495,496,497,494,492,493,501,502,503,500,498,499,84,85,86,87,88,89,90,91,92,93,94,95,672,696,691,699,260,259,258,262,263,261,257,255,256,253,254,252,265,266,264,268,269,267,271,272,270,274,275,273,618,619,620,621,622,623,616,617,615,612,613,614,629,627,628,625,626,624,635,633,634,631,632,630,200,198,199,203,201,202,195,196,197,194,192,193,662,678,669,685,141,143,142,139,140,138,134,132,133,137,135,136,175,176,174,178,179,177,173,171,172,169,170,168,186,187,188,189,190,191,184,185,183,180,181,182,121,122,120,124,125,123,127,128,126,130,131,129,282,283,284,285,286,287,280,281,279,276,277,278,660,682,668,688,209,208,207,204,205,206,214,215,213,210,211,212,225,226,227,224,222,223,216,217,218,219,220,221,239,237,238,235,236,234,230,228,229,233,231,232,241,242,240,244,245,243,247,248,246,250,251,249,645,646,647,644,642,643,636,637,638,639,640,641,663,677,667,684,466,465,467,464,462,463,456,457,458,459,460,461,470,468,469,473,471,472,476,474,475,479,477,478,580,581,579,576,577,578,586,587,585,582,583,584,447,448,449,446,444,445,453,454,455,452,450,451,62,60,61,65,63,64,68,66,67,71,69,70,661,679,671,686 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {64} 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 20:01:54 · history