Equation 677 Database

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Magma 60c1d835557a…

magma 60c1d835557a
Size
705
Isomorphism class hash
60c1d835557ae94ce979054ff2aaa29de1a1a78fbd8ef9966c8bbf4aa961c57e
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 20:07:35
Display reorder
660,259,652,657,653,647,260,613,612,617,607,258,633,632,637,627,573,262,572,577,567,593,263,592,597,587,553,261,552,557,547,477,472,257,473,467,435,430,255,431,427,457,452,256,453,447,532,537,253,533,527,492,497,254,493,487,512,517,252,513,507,695,701,698,689,217,645,644,648,649,218,608,605,604,609,216,628,625,624,629,568,220,565,564,569,588,221,585,584,589,548,219,545,544,549,464,465,223,468,469,424,425,224,428,429,444,445,222,448,449,525,524,226,528,529,485,484,227,488,489,505,504,225,508,509,700,704,696,694,4,210,231,395,251,5,393,211,232,249,3,394,212,233,250,391,1,213,230,247,392,0,214,228,248,390,2,215,229,246,237,208,10,386,242,238,209,11,384,240,239,207,9,385,241,204,236,6,389,245,205,234,7,387,243,206,235,8,388,244,678,681,675,663,135,172,158,43,419,136,44,173,156,417,137,42,171,157,418,46,134,168,161,415,47,132,169,159,416,45,133,170,160,414,164,178,141,41,410,162,179,142,39,408,163,177,143,40,409,174,167,140,37,413,175,165,138,38,411,176,166,139,36,412,662,670,684,668,64,651,656,650,642,65,610,611,616,602,63,630,631,636,622,570,60,571,576,562,590,61,591,596,582,550,62,551,556,542,476,471,70,470,462,434,439,71,438,437,456,451,69,450,442,531,536,66,530,522,491,496,67,490,482,511,516,68,510,502,690,685,688,702,184,655,659,641,646,185,601,615,619,606,183,621,635,639,626,561,180,575,579,566,580,181,595,599,586,541,182,555,559,546,479,475,190,460,466,420,433,191,421,426,459,455,189,440,446,535,539,186,521,526,495,499,187,481,486,515,519,188,501,506,699,697,687,692,89,658,643,640,654,87,600,618,603,614,88,620,638,623,634,560,85,578,563,574,581,86,598,583,594,540,84,558,543,554,463,478,95,461,474,423,436,93,422,432,443,458,94,441,454,538,523,91,520,534,498,483,92,480,494,518,503,90,500,514,693,686,691,703,148,323,126,371,407,149,369,321,127,405,147,370,322,128,406,367,144,319,129,403,368,145,320,130,404,366,146,318,131,402,124,314,154,362,398,125,312,155,360,396,123,313,153,361,397,317,120,150,365,401,315,121,151,363,399,316,122,152,364,400,669,679,683,671,198,17,24,311,335,199,309,15,25,333,200,310,16,26,334,307,201,13,27,331,308,202,14,28,332,306,203,12,29,330,30,23,196,302,326,31,21,197,300,324,32,22,195,301,325,19,33,192,305,329,20,34,193,303,327,18,35,194,304,328,676,666,673,682,49,284,275,299,383,50,297,282,273,381,48,298,283,274,382,295,52,287,271,379,296,53,285,272,380,294,51,286,270,378,266,279,55,290,374,264,280,56,288,372,265,281,54,289,373,278,269,58,293,377,276,267,59,291,375,277,268,57,292,376,664,665,680,661,83,359,111,347,97,81,345,357,112,98,82,346,358,113,96,343,79,355,110,100,344,80,356,108,101,342,78,354,109,99,117,350,74,338,103,118,348,72,336,104,119,349,73,337,102,353,116,77,341,106,351,114,75,339,107,352,115,76,340,105,667,674,672,677 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#ba7c5b5fc3c8b2f23fa53f03c835320f8b0f039ca1c741e1670481476e08a637, 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 20:07:36 · history