Equation 677 Database

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Magma 6c34c96ca584…

magma 6c34c96ca584
Size
705
Isomorphism class hash
6c34c96ca584b8e793ff01176ce0f07466a55c62f991dc28f3e34dc2e8a6f632
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 17:28:36
Display reorder
660,59,474,465,462,464,434,429,57,423,421,445,457,58,446,442,55,537,525,526,522,56,497,485,486,482,54,517,505,506,502,50,597,585,586,580,48,557,545,546,540,49,577,565,566,560,657,53,645,646,641,606,617,51,605,600,637,52,625,626,621,698,685,696,690,143,472,466,461,473,426,427,141,424,420,456,454,142,447,441,139,534,536,527,520,140,494,496,487,481,138,514,516,507,501,134,594,596,587,582,132,554,556,547,542,133,574,576,567,562,654,137,656,647,642,607,614,135,616,602,634,136,636,627,622,694,697,693,687,311,145,398,326,281,146,279,309,396,324,280,144,310,397,325,307,148,277,401,329,308,149,278,399,327,306,147,276,400,328,302,151,287,404,332,300,152,285,402,330,301,150,286,403,331,154,305,283,407,335,405,155,303,284,333,153,304,282,406,334,674,662,666,678,191,212,218,28,362,210,360,189,216,29,361,211,190,217,27,187,215,365,221,24,188,213,363,219,25,186,214,364,220,26,182,207,368,224,34,180,208,366,222,35,181,209,367,223,33,206,185,371,227,30,225,204,183,369,31,205,184,370,226,32,681,671,683,661,8,475,460,467,470,435,433,6,428,430,451,459,7,440,448,11,539,531,521,528,9,499,491,480,488,10,519,511,500,508,3,599,591,581,588,4,559,551,541,548,5,579,571,561,568,659,2,651,640,648,601,619,1,611,608,639,0,631,620,628,699,691,703,689,244,478,477,476,479,438,439,245,437,436,458,455,243,444,453,240,535,538,524,533,241,495,498,484,493,242,515,518,504,513,250,595,598,584,593,251,555,558,544,553,249,575,578,564,573,655,246,658,644,653,604,615,247,618,613,635,248,638,624,633,688,700,695,686,192,463,468,469,471,422,425,193,431,432,452,443,194,449,450,195,523,532,529,530,196,483,492,489,490,197,503,512,509,510,198,583,592,589,590,199,543,552,549,550,200,563,572,569,570,643,201,652,649,650,609,603,202,612,610,623,203,632,629,630,702,692,704,701,92,374,386,169,164,372,162,90,384,170,163,373,91,385,168,95,377,167,389,172,93,375,165,387,173,94,376,166,388,171,87,380,159,392,175,88,378,160,390,176,89,379,161,391,174,383,86,158,395,178,393,381,84,156,179,382,85,157,394,177,673,669,663,675,20,105,235,314,410,106,408,18,236,312,409,107,19,234,313,23,104,413,238,317,21,102,411,239,315,22,103,412,237,316,15,96,416,233,320,16,97,414,231,318,17,98,415,232,319,99,14,419,229,323,230,100,12,417,321,101,13,418,228,322,672,679,665,684,288,256,268,129,338,257,336,289,269,130,337,255,290,267,131,291,252,341,264,128,292,253,339,265,126,293,254,340,266,127,294,262,344,274,120,295,263,342,275,121,296,261,343,273,122,258,297,347,270,123,271,259,298,345,124,260,299,346,272,125,676,667,664,680,119,350,61,44,74,348,72,117,62,42,73,349,118,60,43,115,353,77,64,47,116,351,75,65,45,114,352,76,63,46,110,356,80,67,39,108,354,78,68,40,109,355,79,66,41,359,113,83,70,38,71,357,111,81,36,358,112,82,69,37,668,682,670,677 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#57f0a2716884c2711bcb20a2573985b973a13e807353fc83680d5538f9af708e, 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 17:28:37 · history