Equation 677 Database

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Magma 9cbf8ea1190b…

magma 9cbf8ea1190b
Size
705
Isomorphism class hash
9cbf8ea1190b86c9ec0ab198a7d42ba1f0229a50d09f40fb8959680b1f67649d
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 16:39:06
Display reorder
660,44,550,557,558,551,571,570,42,577,578,590,591,43,597,598,611,47,610,617,618,45,631,630,637,638,651,46,650,657,658,511,39,510,517,518,531,40,530,537,538,497,491,41,490,498,38,424,423,427,428,36,450,449,455,456,37,470,469,475,476,696,699,688,687,300,553,556,559,554,574,573,301,576,579,593,594,302,596,599,614,303,613,616,619,304,634,633,636,639,654,305,653,656,659,514,306,513,516,519,534,307,533,536,539,496,494,308,493,499,309,437,436,426,429,310,453,452,454,457,311,473,472,474,477,693,702,692,690,67,262,275,276,240,241,263,68,273,277,261,242,66,274,278,243,70,258,271,279,71,244,259,272,280,245,69,260,270,281,246,65,253,266,282,247,63,254,264,283,265,248,64,252,284,61,249,256,269,285,62,250,257,267,286,60,251,255,268,287,663,661,676,673,333,342,128,20,402,403,343,334,126,18,344,404,335,127,19,405,332,345,131,23,330,406,346,129,21,407,331,347,130,22,400,324,340,123,15,401,325,341,124,16,125,399,326,339,17,327,396,336,122,14,328,397,337,120,12,329,398,338,121,13,677,674,679,665,296,543,549,542,547,567,563,294,569,562,583,587,295,589,582,607,299,603,609,602,297,627,623,629,622,647,298,643,649,642,507,291,504,509,503,527,292,524,529,523,489,487,293,484,483,290,422,420,435,432,288,447,443,448,442,289,467,464,468,463,695,704,700,697,1,540,541,545,546,566,560,0,561,565,580,586,2,581,585,606,3,601,600,605,4,626,621,620,625,646,5,641,640,645,506,6,500,501,505,526,7,520,521,525,480,486,8,481,485,9,434,430,431,433,10,446,441,440,445,11,466,461,460,465,698,701,703,694,28,548,544,552,555,575,568,29,564,572,588,595,27,584,592,615,24,608,604,612,25,635,628,624,632,655,26,648,644,652,515,34,508,502,512,535,35,528,522,532,482,495,33,488,492,30,438,439,421,425,31,459,458,444,451,32,478,479,462,471,686,691,689,685,238,75,354,318,86,84,76,239,355,319,77,85,237,356,320,89,234,74,357,321,235,87,72,358,322,88,236,73,359,323,92,229,81,352,316,90,230,82,353,317,351,91,228,83,315,232,95,80,348,312,233,93,78,349,313,231,94,79,350,314,668,662,666,680,56,178,190,203,205,206,179,54,191,201,177,204,55,189,202,208,59,174,186,199,57,209,175,187,200,207,58,176,188,198,211,51,169,181,194,212,52,170,182,192,180,210,53,168,193,50,214,172,184,197,48,215,173,185,195,49,213,171,183,196,675,684,671,667,134,366,113,390,414,415,367,132,111,391,368,416,133,112,392,417,137,369,109,393,135,418,370,110,394,419,136,371,108,395,412,140,364,119,388,413,138,365,117,389,118,411,139,363,387,143,408,360,115,384,141,409,361,116,385,142,410,362,114,386,683,678,682,670,103,151,161,378,220,221,152,104,159,379,150,219,102,160,380,216,106,154,157,381,107,217,155,158,382,218,105,153,156,383,226,101,149,167,376,227,99,147,165,377,166,225,100,148,375,97,222,145,163,372,98,223,146,164,373,96,224,144,162,374,681,672,669,664 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#3866b47acdf4717a31e27879d6448be53ada0b89c1671a7aec66e55c44000764, 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 16:39:08 · history