Equation 677 Database

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Magma b1f31a9e4c23…

magma b1f31a9e4c23
Size
705
Isomorphism class hash
b1f31a9e4c23662722959ccd373cc47279c62281726aa4843404bb0749d00c7e
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 16:30:37
Display reorder
660,59,454,450,445,448,57,468,474,470,465,425,423,58,432,428,508,55,514,510,505,528,56,534,530,525,488,54,494,490,485,50,578,569,571,565,48,598,589,591,585,49,558,549,551,545,638,53,629,631,625,658,51,649,651,645,618,52,609,611,605,688,696,698,690,231,451,449,455,444,232,464,471,469,475,424,422,233,431,435,504,230,511,509,515,524,228,531,529,535,484,229,491,489,495,237,574,564,570,579,238,594,584,590,599,239,554,544,550,559,634,236,624,630,639,654,234,644,650,659,614,235,604,610,619,687,702,693,697,227,409,46,361,373,225,374,410,47,362,408,372,226,45,360,376,223,412,42,364,377,224,413,43,365,375,222,411,44,363,218,415,379,37,367,216,416,380,38,368,217,414,378,36,366,418,221,382,40,370,419,219,383,41,371,417,220,381,39,369,662,672,682,674,87,313,275,252,277,88,278,314,273,253,312,276,89,274,254,280,86,316,271,255,281,84,317,272,256,279,85,315,270,257,93,319,283,266,258,94,320,284,264,259,95,318,282,265,260,322,92,286,269,261,323,90,287,267,262,321,91,285,268,263,663,681,667,661,69,453,459,456,446,70,466,473,479,476,434,429,71,439,436,506,68,513,519,517,526,66,533,539,538,486,67,493,499,497,60,577,566,575,568,61,597,586,595,588,62,557,546,555,548,637,63,626,635,628,657,64,646,655,648,617,65,606,615,608,685,686,695,700,83,457,441,452,458,81,478,477,461,472,437,438,82,426,433,518,79,516,500,512,536,80,537,521,532,498,78,496,480,492,74,573,572,561,576,72,593,592,581,596,73,553,552,540,556,633,77,632,620,636,653,75,652,640,656,613,76,612,601,616,704,692,689,694,138,447,443,442,440,139,460,467,463,462,430,427,140,421,420,501,141,507,503,502,520,142,527,523,522,481,143,487,483,482,136,567,560,563,562,137,587,580,583,582,135,547,541,543,542,627,132,621,623,622,647,133,641,643,642,607,134,600,603,602,699,701,691,703,3,301,185,385,109,4,110,302,183,386,300,108,5,184,384,112,2,304,181,388,113,1,305,182,389,111,0,303,180,387,9,307,115,191,391,10,308,116,189,392,11,306,114,190,390,310,8,118,187,394,311,6,119,188,395,309,7,117,186,393,676,679,666,670,204,144,14,166,289,205,290,145,12,167,146,288,206,13,165,292,207,147,17,162,293,208,148,15,163,291,209,149,16,164,210,150,295,20,157,211,151,296,18,158,212,152,294,19,156,153,213,298,23,160,154,214,299,21,161,155,215,297,22,159,665,677,671,664,251,31,337,331,105,249,106,32,338,332,30,107,250,336,330,104,247,34,340,334,102,248,35,341,335,103,246,33,339,333,242,29,96,343,329,240,27,97,344,327,241,28,98,342,328,25,245,99,346,325,26,243,100,347,326,24,244,101,345,324,668,683,675,673,169,397,349,201,121,170,122,398,350,202,396,120,168,348,203,124,172,400,352,200,125,173,401,353,198,123,171,399,351,199,175,403,127,355,192,176,404,128,356,193,174,402,126,354,194,406,178,130,358,195,407,179,131,359,196,405,177,129,357,197,669,678,680,684 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#34588157c307db5531c4fa8d738de6f4f43dd6ced943a299dd02fbb5d9b36bf1, 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 16:30:38 · history