Equation 677 Database

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Magma 42d8be552c00…

magma 42d8be552c00
Size
705
Isomorphism class hash
42d8be552c00235dfac3052b95dcc1658763e11aae959b7c76438e561b1cce58
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 21:54:37
Display reorder
660,296,346,360,359,451,294,452,347,361,357,295,450,345,362,358,454,299,342,363,355,455,297,343,364,356,453,298,344,365,354,449,291,337,366,350,447,292,338,367,348,448,293,336,368,349,290,445,340,369,353,288,446,341,370,351,289,444,339,371,352,663,667,668,666,212,415,98,128,57,210,58,416,96,126,211,59,414,97,127,56,215,418,101,131,54,213,419,99,129,55,214,417,100,130,48,207,413,104,123,49,208,411,102,124,50,209,412,103,125,206,51,409,107,122,204,52,410,105,120,205,53,408,106,121,686,688,687,685,323,273,379,29,495,321,496,274,380,27,322,494,275,378,28,498,319,272,382,25,499,320,270,383,26,497,318,271,381,24,493,314,264,377,35,491,312,265,375,33,492,313,266,376,34,317,489,267,373,31,315,490,268,374,32,316,488,269,372,30,662,661,669,670,70,483,427,471,222,71,223,484,428,472,69,224,482,426,470,225,66,486,430,474,226,67,487,431,475,227,68,485,429,473,220,61,481,425,469,221,62,479,423,467,219,60,480,424,468,64,216,477,421,465,65,217,478,422,466,63,218,476,420,464,675,674,677,673,38,587,391,403,586,36,588,589,392,404,37,584,585,390,402,592,41,593,394,406,594,39,595,395,407,590,40,591,393,405,583,44,582,389,401,579,42,578,387,399,581,43,580,388,400,47,575,574,385,397,45,577,576,386,398,46,573,572,384,396,665,664,671,672,310,439,563,562,263,311,261,440,565,564,309,262,438,560,561,259,306,442,568,569,260,307,443,571,570,258,308,441,566,567,254,301,437,559,558,252,302,435,554,555,253,300,436,556,557,304,257,433,550,551,305,255,434,553,552,303,256,432,548,549,698,697,695,693,76,72,88,463,515,77,647,646,645,644,78,523,522,89,462,655,79,654,653,652,659,80,658,657,656,651,81,650,649,648,520,82,521,94,461,517,83,516,95,459,518,84,519,93,460,85,512,73,90,457,86,513,74,91,458,87,514,75,92,456,702,701,704,703,191,21,634,635,251,189,249,22,637,636,190,250,23,632,633,247,187,20,640,641,248,188,18,643,642,246,186,19,638,639,242,182,12,631,630,240,180,13,627,626,241,181,14,629,628,185,245,15,623,622,183,243,16,624,625,184,244,17,621,620,700,699,696,694,110,611,538,539,610,108,613,612,540,541,109,608,609,537,536,616,113,617,545,544,618,111,619,546,547,614,112,615,543,542,607,116,606,534,535,603,114,602,531,530,605,115,604,533,532,119,599,598,527,526,117,600,601,528,529,118,597,596,525,524,680,679,683,684,203,133,157,145,507,201,508,134,158,146,202,506,132,156,144,510,199,136,160,148,511,200,137,161,149,509,198,135,159,147,505,194,139,163,151,503,192,140,164,152,504,193,138,162,150,197,501,142,166,154,195,502,143,167,155,196,500,141,165,153,681,682,676,678,8,178,287,332,238,6,239,179,285,330,7,237,177,286,331,234,11,174,283,335,235,9,175,284,333,236,10,176,282,334,229,3,169,278,327,230,4,170,276,328,228,5,168,277,329,2,232,172,281,326,1,233,173,279,324,0,231,171,280,325,689,690,692,691 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#fba993da3569b4910e46b63a02193464b761c68efe01dd1a285b47fabe43afe4, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 21:54:38 · history