Equation 677 Database

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Magma 596be40d916d…

magma 596be40d916d
Size
705
Isomorphism class hash
596be40d916d8bd19682fa012fd55571dbf364d1b8f6117847dc4f7b8f8df317
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 21:23:13
Display reorder
660,473,52,460,462,461,433,53,428,421,420,456,51,442,441,440,536,48,522,521,520,496,49,482,480,481,516,50,502,501,500,58,596,581,582,580,59,556,540,542,541,57,576,561,562,560,656,54,640,642,641,616,55,601,602,600,636,56,620,622,621,698,695,693,692,468,215,472,465,466,425,213,427,422,423,448,214,445,452,446,529,211,533,526,527,489,212,493,486,487,509,210,513,506,507,206,589,593,586,587,204,549,553,546,547,205,569,573,566,567,649,209,653,646,647,609,207,613,606,607,629,208,633,626,627,685,694,687,690,175,259,284,46,290,176,260,282,47,288,174,258,45,283,289,178,262,287,42,293,179,263,285,43,291,177,261,286,44,292,257,173,279,37,296,255,171,280,38,294,256,172,281,36,295,169,253,278,40,299,170,254,276,41,297,168,252,277,39,298,662,675,661,664,145,69,107,87,338,146,70,105,88,336,144,71,89,106,337,148,68,103,86,341,149,66,104,84,339,147,67,102,85,340,60,151,98,93,344,61,152,96,94,342,62,150,97,95,343,154,63,101,92,347,155,64,99,90,345,153,65,100,91,346,683,674,669,672,474,196,464,471,463,434,197,430,432,429,458,195,451,444,443,538,192,525,532,524,498,193,485,492,484,518,194,505,512,504,202,598,585,592,584,203,558,545,552,544,201,578,565,572,564,658,198,645,652,644,618,199,605,612,604,638,200,625,632,624,702,699,703,691,476,24,477,478,479,437,25,438,439,436,455,26,457,453,454,523,27,534,537,535,483,28,494,497,495,503,29,514,517,515,30,583,594,597,595,31,543,554,557,555,32,563,574,577,575,643,33,654,657,655,603,34,614,617,615,623,35,634,637,635,701,696,697,700,469,110,467,475,470,426,108,424,435,431,449,109,459,447,450,530,113,528,539,531,490,111,488,499,491,510,112,508,519,511,116,590,588,599,591,114,550,548,559,551,115,570,568,579,571,650,119,648,659,651,610,117,608,619,611,630,118,628,639,631,689,688,704,686,225,187,302,230,244,226,188,300,228,245,227,186,229,301,243,224,190,305,233,240,222,191,303,231,241,223,189,304,232,242,185,216,308,236,250,183,217,306,234,251,184,218,307,235,249,219,181,311,239,246,220,182,309,237,247,221,180,310,238,248,678,665,668,680,135,164,75,410,350,136,162,76,408,348,137,163,409,77,349,134,167,74,413,353,132,165,72,411,351,133,166,73,412,352,159,141,81,416,356,160,142,82,414,354,161,143,83,415,355,140,158,80,419,359,138,156,78,417,357,139,157,79,418,358,663,682,670,684,326,266,374,19,398,324,264,372,20,396,325,265,18,373,397,329,269,377,22,401,327,267,375,23,399,328,268,376,21,400,272,332,380,17,404,270,330,378,15,402,271,331,379,16,403,335,275,383,13,407,333,273,381,14,405,334,274,382,12,406,667,676,679,681,362,6,314,386,121,360,7,312,384,122,361,8,385,313,120,365,9,317,389,124,363,10,315,387,125,364,11,316,388,123,4,368,320,392,127,5,366,318,390,128,3,367,319,391,126,371,1,323,395,130,369,0,321,393,131,370,2,322,394,129,671,666,673,677 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#edd749230bc58665165cb5ff86cf593765d0cefcd490b689f1cd7ce77c95b856, 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 21:23:14 · history