Equation 677 Database

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Magma 63f0443958be…

magma 63f0443958be
Size
705
Isomorphism class hash
63f0443958be3d1085b1b93bbaa40b9903a656f22e711740484c4eb97534a4f8
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 19:49:32
Display reorder
704,204,162,171,189,163,205,172,190,164,206,173,191,207,165,170,188,208,166,168,186,209,167,169,187,160,177,210,180,161,178,211,181,159,179,212,182,176,156,213,183,174,157,214,184,175,158,215,185,193,194,192,196,197,195,199,200,201,202,203,198,702,703,701,700,658,659,656,657,651,650,649,648,655,654,653,652,642,643,641,640,646,647,644,645,638,639,637,636,623,620,622,621,615,612,614,613,619,616,618,617,632,635,634,633,624,627,626,625,628,631,630,629,21,22,23,20,18,19,12,13,17,15,16,14,688,690,689,691,436,0,404,419,2,437,402,417,1,435,403,418,432,4,407,415,433,5,405,416,434,3,406,414,7,399,442,410,8,400,443,408,6,401,441,409,398,10,438,413,396,11,439,411,397,9,440,412,427,428,426,430,431,429,425,423,420,421,422,424,673,674,672,675,287,342,248,262,343,285,246,263,344,286,247,261,283,345,251,258,284,346,249,259,282,347,250,260,340,243,278,253,341,244,276,254,339,245,277,252,242,336,281,256,240,337,279,257,241,338,280,255,270,271,272,273,274,275,268,269,266,264,265,267,682,680,683,681,140,59,155,111,57,138,153,112,58,139,154,113,143,55,151,110,141,56,152,108,142,54,150,109,50,146,135,117,48,144,136,118,49,145,137,119,149,53,134,116,147,51,132,114,148,52,133,115,131,129,130,127,128,126,122,120,124,125,123,121,695,694,692,693,308,224,322,330,222,306,323,331,223,307,321,332,311,227,318,333,309,225,319,334,310,226,320,335,219,313,303,328,220,314,304,329,221,312,305,327,316,218,302,324,317,216,300,325,315,217,301,326,299,297,298,295,296,294,290,288,292,293,291,289,696,699,697,698,532,34,543,562,35,533,544,563,33,531,545,561,528,30,542,558,529,31,540,559,530,32,541,560,25,549,538,553,26,550,539,554,24,551,537,552,548,28,534,556,546,29,535,557,547,27,536,555,521,519,520,517,518,516,527,525,522,523,524,526,685,687,684,686,72,46,84,97,47,73,85,98,45,74,86,96,75,42,87,100,76,43,88,101,77,44,89,99,37,90,78,103,38,91,79,104,36,92,80,102,93,40,81,106,94,41,82,107,95,39,83,105,61,62,60,64,65,63,67,68,69,70,71,66,662,660,663,661,359,239,366,375,237,357,367,376,238,358,368,377,355,235,369,374,356,236,370,372,354,234,371,373,230,364,350,381,228,365,348,382,229,363,349,383,360,233,353,380,361,231,351,378,362,232,352,379,395,393,394,391,392,390,386,384,388,389,387,385,679,677,678,676,491,500,452,466,498,489,450,467,499,490,451,465,487,503,455,462,488,501,453,463,486,502,454,464,495,447,482,457,496,448,480,458,497,449,481,456,446,494,485,460,444,492,483,461,445,493,484,459,474,475,476,477,478,479,472,473,470,468,469,471,666,664,667,665,576,504,590,604,505,577,588,605,506,578,589,603,579,507,593,600,580,508,591,601,581,509,592,602,510,596,582,610,511,594,583,611,512,595,584,609,599,513,585,606,597,514,586,607,598,515,587,608,565,566,564,568,569,567,571,572,573,574,575,570,668,669,671,670 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#adb39c7b26968070fd85ec3ca227f43c35cfd242a3390aaf8597bfe24e1ed89b, 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 19:49:32 · history