Equation 677 Database

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Magma aefd170c7a98…

magma aefd170c7a98
Size
705
Isomorphism class hash
aefd170c7a98942659c8f54e15d185f0a985f2b321990d34bab912e0a781cc47
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 19:47:09
Display reorder
704,130,78,111,100,131,79,112,101,129,80,113,99,126,81,110,96,127,82,108,97,128,83,109,98,76,121,106,117,77,122,107,118,75,120,105,119,72,124,102,116,73,125,103,114,74,123,104,115,85,86,84,88,89,87,91,92,93,94,95,90,700,701,703,702,656,657,658,659,648,650,651,649,652,654,655,653,641,640,643,642,644,645,647,646,637,636,639,638,621,620,622,623,613,612,614,615,617,616,618,619,633,632,634,635,625,624,626,627,629,628,630,631,336,337,338,339,340,341,342,343,347,345,346,344,691,689,690,688,335,21,317,304,333,22,315,305,334,23,316,303,331,20,313,300,332,18,314,301,330,19,312,302,12,326,310,323,13,324,311,321,14,325,309,322,15,329,306,319,16,327,307,320,17,328,308,318,289,290,288,292,293,291,295,296,297,298,299,294,675,672,674,673,215,59,197,228,213,57,195,229,214,58,196,230,211,55,193,231,212,56,194,232,210,54,192,233,50,206,234,203,48,204,235,201,49,205,236,202,53,209,237,199,51,207,238,200,52,208,239,198,221,219,220,217,218,216,227,225,222,223,224,226,681,683,680,682,373,446,370,357,374,444,371,358,372,445,369,359,376,449,366,356,377,447,367,354,375,448,368,355,452,379,348,361,450,380,349,362,451,378,350,360,455,382,351,364,453,383,352,365,454,381,353,363,393,394,395,392,390,391,384,385,389,387,388,386,693,692,694,695,154,136,180,168,155,137,181,169,153,135,182,170,150,132,183,171,151,133,184,172,152,134,185,173,142,145,174,186,143,146,175,187,141,144,176,188,138,148,177,189,139,149,178,190,140,147,179,191,160,161,159,156,157,158,166,167,164,162,163,165,698,697,699,696,595,68,577,565,596,66,578,566,594,67,576,564,598,71,580,568,599,69,581,569,597,70,579,567,63,593,571,583,64,591,572,584,65,592,570,582,62,589,574,586,60,590,575,587,61,588,573,585,557,555,556,553,554,552,563,561,558,559,560,562,686,684,687,685,429,45,412,401,430,46,413,399,431,47,411,400,428,44,408,397,426,42,409,398,427,43,410,396,36,420,407,418,37,421,405,419,38,422,406,417,39,423,403,414,40,424,404,415,41,425,402,416,436,437,435,432,433,434,442,443,440,438,439,441,661,663,660,662,257,3,248,285,255,4,246,286,256,5,247,287,253,2,251,284,254,1,249,282,252,0,250,283,9,263,276,243,10,261,277,244,11,262,278,245,8,259,279,242,6,260,280,240,7,258,281,241,271,272,270,274,275,273,269,267,264,265,266,268,676,678,677,679,500,25,482,468,498,26,480,469,499,24,481,470,503,28,485,471,501,29,483,472,502,27,484,473,31,495,474,488,32,496,475,486,30,497,476,487,34,494,477,491,35,492,478,489,33,493,479,490,460,461,459,456,457,458,466,467,464,462,463,465,665,667,664,666,515,604,541,529,513,605,542,530,514,603,540,528,511,600,544,532,512,601,545,533,510,602,543,531,610,506,535,547,611,504,536,548,609,505,534,546,606,509,538,550,607,507,539,551,608,508,537,549,521,519,520,517,518,516,527,525,522,523,524,526,670,671,669,668 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#a9f62e2491236cd33b6e554b1a4dc1a2938062e1ffa7bd655365fbe4324c4209, 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 19:47:10 · history