Equation 677 Database

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Magma f345e3bb756f…

magma f345e3bb756f
Size
705
Isomorphism class hash
f345e3bb756f99fd2f206727d0382dfc4dc2fbdcdc8b7a5435017c9f4c7e0408
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 15:24:09
Display reorder
704,436,435,437,438,424,425,426,427,428,429,430,431,432,433,434,453,439,440,441,442,443,444,445,446,447,448,449,450,451,452,456,457,458,459,460,461,462,463,464,465,466,467,468,454,473,474,475,476,477,478,479,480,481,482,483,469,470,471,472,455,701,700,702,703,656,659,658,657,634,635,636,637,638,639,60,61,62,63,655,645,646,647,648,649,650,651,652,653,654,640,641,642,643,644,631,632,633,619,620,621,622,623,624,625,626,627,628,629,608,609,610,611,612,613,614,615,616,617,618,604,605,606,607,630,689,691,690,688,208,207,209,210,211,212,213,199,200,201,202,203,204,205,206,191,192,193,194,195,196,197,198,184,185,186,187,188,189,190,240,241,242,243,229,230,231,232,233,234,235,236,237,238,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,239,673,672,674,675,342,341,343,344,345,346,347,348,334,335,336,337,338,339,340,362,363,349,350,351,352,353,354,355,356,357,358,359,360,361,333,319,320,321,322,323,324,325,326,327,328,329,330,331,316,317,318,304,305,306,307,308,309,310,311,312,313,314,315,332,682,683,680,681,116,115,117,118,119,120,121,122,123,109,110,111,112,113,114,108,94,95,96,97,98,99,100,101,102,103,104,105,106,107,76,77,78,64,65,66,67,68,69,70,71,72,73,74,93,79,80,81,82,83,84,85,86,87,88,89,90,91,92,75,694,695,692,693,367,366,368,369,370,371,372,373,374,375,376,377,378,364,365,387,388,389,390,391,392,393,379,380,381,382,383,384,385,386,408,394,395,396,397,398,399,400,401,402,403,404,405,406,416,417,418,419,420,421,422,423,409,410,411,412,413,414,415,407,699,698,696,697,496,495,497,498,484,485,486,487,488,489,490,491,492,493,494,513,499,500,501,502,503,504,505,506,507,508,509,510,511,512,516,517,518,519,520,521,522,523,524,525,526,527,528,514,533,534,535,536,537,538,539,540,541,542,543,529,530,531,532,515,686,685,684,687,162,161,163,164,165,166,167,168,154,155,156,157,158,159,160,182,183,169,170,171,172,173,174,175,176,177,178,179,180,181,153,139,140,141,142,143,144,145,146,147,148,149,150,151,136,137,138,124,125,126,127,128,129,130,131,132,133,134,135,152,660,661,663,662,258,257,244,245,246,247,248,249,250,251,252,253,254,255,256,266,267,268,269,270,271,272,273,259,260,261,262,263,264,265,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,274,679,678,677,676,18,17,19,20,21,22,23,24,25,26,27,28,29,15,16,13,14,1,0,2,3,4,5,6,7,8,9,10,11,12,59,45,46,47,48,49,50,51,52,53,54,55,56,57,42,43,44,30,31,32,33,34,35,36,37,38,39,40,41,58,667,666,665,664,602,601,603,589,590,591,592,593,594,595,596,597,598,599,600,582,583,584,585,586,587,588,574,575,576,577,578,579,580,581,553,554,555,556,557,558,544,545,546,547,548,549,550,551,561,562,563,564,565,566,567,568,569,570,571,572,573,559,560,552,669,668,670,671 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#17d8eb76b6bf5b6d0c7c94cbffab8bf30c3f61585a1079f6e7ebccc76f8bf7d1, 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 15:24:12 · history