Equation 677 Database

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Magma 8256dbacc3dc…

magma 8256dbacc3dc
Size
705
Isomorphism class hash
8256dbacc3dce8b35b9dde68a317132ef09c613385a453790d1a504e878c7aba
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 16:26:00
Display reorder
660,537,520,528,8,525,497,480,488,6,485,517,500,508,7,505,444,457,448,11,445,460,477,468,9,465,436,429,431,10,423,657,3,640,648,645,617,4,601,608,605,637,5,621,628,625,2,577,561,568,565,1,597,580,588,585,0,557,541,548,545,703,685,690,699,536,521,530,98,523,496,481,490,96,483,516,501,510,97,503,441,456,450,101,442,461,476,470,99,463,427,420,425,100,422,656,104,641,650,643,616,102,600,610,603,636,103,620,630,623,107,576,560,570,563,105,596,581,590,583,106,556,540,550,543,704,700,694,697,287,293,401,57,119,285,291,399,58,117,286,292,400,59,118,289,283,397,56,115,290,284,398,54,116,282,288,396,55,114,278,48,299,407,110,276,49,297,405,108,277,50,298,406,109,51,281,295,403,113,52,279,296,404,111,53,280,294,402,112,684,680,661,674,20,306,329,76,312,18,307,327,77,313,19,308,328,75,314,309,23,325,72,315,310,21,326,73,316,22,311,324,74,317,15,82,304,335,318,16,83,305,333,319,17,81,303,334,320,78,14,300,331,321,79,12,301,332,322,80,13,302,330,323,662,663,670,683,532,522,527,42,539,492,482,487,43,499,512,502,507,44,519,440,452,447,45,459,462,472,467,46,479,426,421,424,47,439,652,40,642,647,659,612,41,602,607,619,632,39,622,627,639,36,572,562,567,579,37,592,582,587,599,38,552,542,547,559,691,688,686,693,534,533,538,169,529,494,493,498,170,489,514,513,518,168,509,453,454,458,172,449,473,474,478,173,469,434,433,437,171,438,654,175,653,658,649,614,176,613,618,609,634,174,633,638,629,178,574,573,578,569,179,594,593,598,589,177,554,553,558,549,689,698,701,695,524,535,531,183,526,484,495,491,184,486,504,515,511,185,506,455,443,451,182,446,475,464,471,180,466,428,435,432,181,430,644,189,655,651,646,604,190,615,611,606,624,191,635,631,626,188,564,575,571,566,186,584,595,591,586,187,544,555,551,546,687,692,696,702,65,377,210,237,26,63,375,211,238,24,64,376,212,239,25,373,61,213,236,29,374,62,214,234,27,60,372,215,235,28,71,228,383,208,32,69,229,381,209,30,70,230,382,207,31,231,67,379,204,35,232,68,380,205,33,233,66,378,206,34,673,679,677,671,123,141,166,265,147,124,142,167,266,148,125,143,165,264,149,140,122,162,268,146,138,120,163,269,144,121,139,164,267,145,129,271,132,157,153,130,272,133,158,154,131,270,134,156,155,274,128,135,160,152,275,126,136,161,150,273,127,137,159,151,668,682,676,666,353,365,413,95,341,351,363,411,93,339,352,364,412,94,340,361,349,409,91,337,362,350,410,92,338,348,360,408,90,336,359,86,371,419,347,357,84,369,417,345,358,85,370,418,346,89,355,367,415,343,87,356,368,416,344,88,354,366,414,342,665,681,675,669,389,222,254,192,248,387,223,252,193,246,388,224,253,194,247,225,385,257,195,251,226,386,255,196,249,384,227,256,197,250,395,198,220,260,243,393,199,221,258,244,394,200,219,259,245,201,391,216,263,242,202,392,217,261,240,203,390,218,262,241,664,667,672,678 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#31b39e995794136cb14e9cfb9c49dab141b331fe9ae7acf51f9a6bc9a2946638, 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 16:26:02 · history