Equation 677 Database

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Magma a12a2023c279…

magma a12a2023c279
Size
705
Isomorphism class hash
a12a2023c2798ea86ed8ab7acd3cae9eff2a21f357efd084832e04e1fcbdb015
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 15:52:40
Display reorder
666,565,564,566,567,568,569,570,571,572,573,574,575,93,94,95,92,90,91,84,85,86,87,88,89,552,553,554,555,556,557,558,559,560,561,562,563,537,538,539,536,534,535,528,529,530,531,532,533,548,546,547,551,549,550,543,544,545,542,540,541,682,697,700,699,152,151,150,154,155,153,149,147,148,145,146,144,634,635,633,630,631,632,625,626,624,628,629,627,140,138,139,143,141,142,135,136,137,134,132,133,194,192,193,197,195,196,200,198,199,203,201,202,131,129,130,127,128,126,122,120,121,125,123,124,686,696,703,694,248,247,246,250,251,249,245,243,244,241,242,240,368,366,367,371,369,370,363,364,365,362,360,361,236,234,235,239,237,238,231,232,233,230,228,229,208,209,207,204,205,206,214,215,213,210,211,212,226,227,225,222,223,224,217,218,216,220,221,219,662,675,670,679,595,594,596,597,598,599,592,593,591,588,589,590,26,24,25,29,27,28,32,30,31,35,33,34,584,582,583,587,585,586,579,580,581,578,576,577,609,610,611,608,606,607,600,601,602,603,604,605,620,618,619,623,621,622,615,616,617,614,612,613,660,673,671,688,480,482,481,485,483,484,488,486,487,491,489,490,458,456,457,461,459,460,464,462,463,467,465,466,518,516,517,521,519,520,524,522,523,527,525,526,501,502,503,500,498,499,492,493,494,495,496,497,512,510,511,515,513,514,507,508,509,506,504,505,683,698,701,692,311,310,309,306,307,308,301,302,300,304,305,303,10,11,9,6,7,8,0,2,1,4,5,3,298,299,297,294,295,296,289,290,288,292,293,291,261,262,263,260,258,259,252,253,254,255,256,257,272,270,271,275,273,274,267,268,269,266,264,265,685,691,702,693,401,400,399,396,397,398,406,407,405,402,403,404,117,118,119,116,114,115,108,109,110,111,112,113,388,389,387,384,385,386,394,395,393,390,391,392,107,105,106,103,104,102,98,96,97,101,99,100,377,375,376,373,374,372,383,381,382,379,380,378,684,690,704,695,55,54,56,57,58,59,52,53,51,48,49,50,282,283,284,285,286,287,280,281,279,276,277,278,44,42,43,47,45,46,39,40,41,38,36,37,69,70,71,68,66,67,60,61,62,63,64,65,79,80,78,82,83,81,77,75,76,73,74,72,665,681,667,687,191,190,189,186,187,188,181,182,180,184,185,183,167,165,166,163,164,162,158,156,157,161,159,160,177,178,179,176,174,175,168,169,170,171,172,173,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,664,677,669,680,408,410,409,413,411,412,416,414,415,419,417,418,471,472,473,470,468,469,477,478,479,476,474,475,445,446,444,448,449,447,451,452,450,454,455,453,429,430,431,428,426,427,420,421,422,423,424,425,440,438,439,443,441,442,435,436,437,434,432,433,661,674,668,689,350,349,348,352,353,351,355,356,354,358,359,357,12,13,14,15,16,17,18,19,20,21,22,23,337,338,336,340,341,339,343,344,342,346,347,345,321,322,323,320,318,319,312,313,314,315,316,317,332,330,331,335,333,334,327,328,329,326,324,325,663,676,672,678 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {63} 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 15:52:41 · history