Equation 677 Database

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Magma 753cdb05572c…

magma 753cdb05572c
Size
705
Isomorphism class hash
753cdb05572ce4bb00e8b73375bb445add5caef05cb0a595af17953b1f985e37
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 19:16:16
Display reorder
660,131,495,487,493,486,515,129,506,507,513,526,130,535,527,533,127,475,466,467,473,128,433,428,429,432,126,455,446,447,453,122,615,606,607,613,120,635,626,627,633,121,655,646,647,653,595,125,586,587,593,547,555,123,546,553,575,124,566,567,573,686,700,696,688,52,491,494,488,481,511,53,501,514,508,521,51,531,534,528,48,471,460,474,468,49,438,434,439,425,50,451,440,454,448,58,611,600,614,608,59,631,620,634,628,57,651,640,654,648,591,54,581,594,588,554,551,55,540,548,571,56,560,574,568,685,692,689,691,46,303,351,168,399,304,47,400,352,169,401,45,305,353,170,42,302,398,350,171,43,300,396,348,172,44,301,397,349,173,37,309,405,357,174,38,310,406,358,175,36,311,407,359,176,308,40,404,356,177,354,306,41,402,178,307,39,403,355,179,664,675,661,669,14,220,230,215,240,221,12,241,228,213,242,13,219,229,214,17,216,243,233,211,15,217,244,231,212,16,218,245,232,210,20,226,246,236,206,18,227,247,234,204,19,225,248,235,205,222,23,249,239,209,237,223,21,250,207,224,22,251,238,208,673,680,672,676,68,489,484,496,485,509,66,505,504,516,525,67,529,524,536,71,469,465,464,476,69,426,424,423,427,70,449,445,444,456,63,609,605,604,616,64,629,625,624,636,65,649,645,644,656,589,62,585,584,596,544,549,60,545,556,569,61,565,564,576,701,702,699,703,150,498,499,492,497,518,151,517,519,512,538,152,537,539,532,153,477,478,479,472,154,421,420,422,431,155,457,458,459,452,148,617,618,619,612,149,638,637,639,632,147,658,657,659,652,597,144,598,599,592,559,558,145,557,552,577,146,578,579,572,697,690,694,687,33,482,483,490,480,502,34,500,503,510,520,35,522,523,530,32,462,461,463,470,30,436,435,437,430,31,442,441,443,450,24,602,601,603,610,25,622,621,623,630,26,642,641,643,650,582,27,580,583,590,543,542,28,541,550,562,29,561,563,570,695,704,693,698,253,88,97,78,387,89,254,388,98,79,389,252,87,96,80,256,84,386,100,81,257,85,384,101,82,255,86,385,99,83,259,94,393,103,76,260,95,394,104,77,258,93,395,102,75,90,262,392,106,72,107,91,263,390,73,92,261,391,105,74,681,674,667,679,167,375,411,139,191,376,165,189,412,140,190,166,377,413,138,163,374,187,410,142,164,372,188,408,143,162,373,186,409,141,158,381,182,417,137,156,382,180,418,135,157,383,181,419,136,380,161,185,416,133,414,378,159,183,134,379,160,184,415,132,671,678,684,677,114,321,327,291,5,322,115,3,328,292,4,116,323,329,293,117,320,0,326,290,118,318,2,324,288,119,319,1,325,289,112,312,11,333,297,113,313,9,334,298,111,314,10,335,299,315,108,7,332,296,330,316,109,8,294,317,110,6,331,295,683,682,663,665,196,363,339,279,273,364,197,274,340,280,275,195,365,341,281,192,362,272,338,278,193,360,270,336,276,194,361,271,337,277,202,369,264,345,285,203,370,265,346,286,201,371,266,347,287,368,198,267,344,284,342,366,199,268,282,367,200,269,343,283,670,668,662,666 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#96b025dbf47c4a59dfaaf1b34262061bd74b6a84a8a9978c39bcd4e78b704a7c, 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 19:16:16 · history