Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma f45308378862…

magma f45308378862
Size
705
Isomorphism class hash
f45308378862ee30f399c5bf9254a31b938acc33d8c589c302d4677442406aeb
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 16:35:34
Display reorder
704,505,1,495,488,496,506,486,0,497,2,504,487,508,494,3,491,509,492,4,489,507,493,5,490,501,6,483,511,502,7,484,512,503,8,485,510,9,500,482,514,10,498,480,515,11,499,481,513,478,479,477,474,475,476,469,470,471,472,473,468,701,700,703,702,657,659,656,658,649,648,650,651,653,655,652,654,640,641,643,642,645,644,647,646,636,637,639,638,620,623,622,621,612,615,614,613,616,619,618,617,635,632,634,633,627,624,626,625,631,628,630,629,82,83,81,78,79,80,73,74,75,76,77,72,690,688,689,691,360,199,351,344,352,361,342,200,353,198,362,343,363,350,202,347,364,348,203,345,365,349,201,346,357,197,339,366,358,195,340,367,359,196,341,368,193,356,338,369,194,354,336,370,192,355,337,371,381,382,383,380,378,379,372,373,377,375,376,374,673,675,674,672,264,222,255,244,256,265,245,223,257,224,266,243,267,254,225,240,268,252,226,241,269,253,227,242,261,220,250,270,262,221,251,271,263,219,249,272,216,260,246,273,217,258,247,274,218,259,248,275,287,285,286,283,284,282,278,276,280,281,279,277,680,682,683,681,138,94,129,119,130,139,117,95,131,93,140,118,141,128,90,115,142,126,91,116,143,127,92,114,120,85,110,136,121,86,108,137,122,84,109,135,88,123,113,132,89,124,111,133,87,125,112,134,105,106,107,104,102,103,96,97,101,99,100,98,694,695,692,693,22,228,59,47,57,23,45,229,58,230,21,46,18,55,231,43,19,56,232,44,20,54,233,42,50,234,38,13,48,235,36,14,49,236,37,12,237,53,41,16,238,51,39,17,239,52,40,15,33,34,35,32,30,31,24,25,29,27,28,26,699,696,697,698,556,466,542,531,540,557,532,467,541,465,555,533,552,545,462,530,553,543,463,528,554,544,464,529,548,457,537,562,546,458,538,563,547,456,539,561,460,551,536,558,461,549,534,559,459,550,535,560,516,517,518,519,520,521,522,523,527,525,526,524,684,686,685,687,185,70,170,159,168,183,160,71,169,69,184,161,181,173,66,158,182,171,67,156,180,172,68,157,176,61,165,191,174,62,166,189,175,60,167,190,64,179,164,187,65,177,162,188,63,178,163,186,150,151,152,153,154,155,148,149,146,144,145,147,660,662,663,661,318,204,307,295,308,319,296,205,306,206,320,294,321,310,207,298,322,311,208,299,323,309,209,297,305,210,293,316,303,211,291,317,304,212,292,315,213,301,289,312,214,302,290,313,215,300,288,314,324,325,326,327,328,329,330,331,335,333,334,332,677,679,678,676,406,432,395,431,393,407,429,433,394,434,405,430,402,391,435,427,403,392,436,428,404,390,437,426,386,438,422,397,384,439,420,398,385,440,421,396,441,389,425,400,442,387,423,401,443,388,424,399,417,418,419,416,414,415,408,409,413,411,412,410,665,667,666,664,582,450,573,603,574,583,604,451,575,452,584,605,585,572,453,602,586,570,454,600,587,571,455,601,564,448,609,580,565,449,610,581,566,447,611,579,444,567,608,576,445,568,606,577,446,569,607,578,588,589,590,591,592,593,594,595,599,597,598,596,669,668,671,670 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#35abc55380bad4d0eeaaa3ec3d1bddd8996633b3da151c70fe1eca862e930666, 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 16:35:35 · history