Equation 677 Database

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Magma f313bca3d8b9…

magma f313bca3d8b9
Size
705
Isomorphism class hash
f313bca3d8b9beb884223f49442df6c1bc8d95f4ff839b0ac26dabc07a690e8e
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 16:55:27
Display reorder
660,536,280,528,531,537,496,491,281,488,497,279,511,516,508,517,453,276,449,451,454,473,277,467,470,474,433,278,427,430,434,648,286,656,651,657,608,287,616,611,617,628,285,636,631,637,282,568,576,571,577,283,588,596,591,597,284,548,556,551,557,691,701,698,685,538,152,520,521,533,498,480,150,481,493,151,501,518,500,513,455,155,440,441,446,475,153,461,460,472,435,154,422,420,432,642,147,658,640,653,602,148,618,600,613,622,149,638,620,633,146,562,578,560,573,144,582,598,581,593,145,542,558,540,553,697,695,690,689,365,54,76,174,298,363,175,55,77,299,56,176,364,75,297,361,57,72,177,294,362,58,73,178,295,360,59,74,179,296,82,52,371,172,289,83,53,369,173,290,81,51,370,171,288,48,78,367,168,292,49,79,368,169,293,50,80,366,170,291,662,672,670,664,24,199,341,256,401,25,257,200,339,399,198,255,26,340,400,27,202,337,252,397,28,203,338,253,398,29,201,336,254,396,347,197,30,262,407,345,195,31,263,405,346,196,32,261,406,193,343,33,258,403,194,344,34,259,404,192,342,35,260,402,682,679,669,666,535,93,522,523,532,495,483,94,482,492,95,503,515,502,512,456,92,447,448,452,478,90,462,463,471,436,91,423,421,431,643,84,655,641,652,603,85,615,601,612,623,86,635,621,632,87,563,575,561,572,88,583,595,580,592,89,543,555,541,552,703,692,699,702,530,268,534,524,539,490,484,269,494,499,267,504,510,514,519,450,264,457,458,459,469,265,476,477,479,429,266,437,438,439,654,274,650,644,659,614,275,610,604,619,634,273,630,624,639,270,574,570,564,579,271,594,590,584,599,272,554,550,544,559,700,693,688,696,527,215,526,525,529,487,485,213,486,489,214,505,507,506,509,444,211,443,442,445,466,212,465,464,468,426,210,425,424,428,646,206,647,645,649,606,204,607,605,609,626,205,627,625,629,209,566,567,565,569,207,586,587,585,589,208,546,547,545,549,704,687,686,694,111,18,96,142,121,112,143,19,97,122,20,141,113,98,120,110,21,99,138,124,108,22,100,139,125,109,23,101,140,123,102,16,117,133,127,103,17,118,134,128,104,15,119,132,126,12,105,116,136,130,13,106,114,137,131,14,107,115,135,129,678,674,676,680,232,43,413,188,71,233,186,44,411,69,42,187,231,412,70,228,46,409,191,67,229,47,410,189,68,230,45,408,190,66,419,41,238,183,62,417,39,239,184,60,418,40,237,185,61,37,415,234,182,65,38,416,235,180,63,36,414,236,181,64,667,677,681,684,305,163,377,329,317,303,327,164,375,315,162,328,304,376,316,301,166,373,325,313,302,167,374,326,314,300,165,372,324,312,383,161,311,335,323,381,159,309,333,321,382,160,310,334,322,157,379,307,331,319,158,380,308,332,320,156,378,306,330,318,665,663,661,671,389,250,353,223,8,387,224,251,351,6,249,222,388,352,7,385,246,349,226,11,386,247,350,227,9,384,248,348,225,10,359,241,395,221,3,357,242,393,219,4,358,240,394,220,5,244,355,391,217,2,245,356,392,218,1,243,354,390,216,0,675,683,673,668 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#48d4131c324a99301720abcc6dab4afc68cf81d40922963883b47bf0604d0986, 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 16:55:28 · history