Equation 677 Database

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Magma 417abd388ffd…

magma 417abd388ffd
Size
705
Isomorphism class hash
417abd388ffd315f7e6cc908f960c91931d53c0d2570b2325b2a43110587e5ca
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 15:10:39
Display reorder
660,327,303,358,340,315,328,316,304,359,341,329,317,305,357,339,314,302,326,354,336,324,312,300,355,337,313,301,325,356,338,309,333,321,349,346,310,334,322,350,347,311,335,323,348,345,332,308,320,352,342,330,306,318,353,343,331,307,319,351,344,685,686,688,687,21,66,402,2,89,22,87,67,403,1,23,88,68,404,0,85,69,20,405,5,18,86,70,406,3,84,71,19,407,4,64,12,95,400,8,65,13,93,401,6,63,14,94,399,7,15,60,91,396,11,16,61,92,397,9,17,62,90,398,10,701,702,704,703,555,288,587,569,588,556,589,289,585,567,557,590,290,586,568,591,291,554,583,565,552,592,292,584,566,593,293,553,582,564,294,561,594,578,575,295,562,595,576,573,296,563,596,577,574,560,297,597,581,571,558,298,598,579,572,559,299,599,580,570,670,669,672,671,446,105,425,411,443,444,441,106,423,412,445,442,107,424,413,439,104,449,421,410,447,440,102,422,408,438,103,448,420,409,96,452,434,431,417,97,450,432,429,418,98,451,433,430,419,455,99,437,427,416,453,100,435,428,414,454,101,436,426,415,680,677,679,678,235,467,129,113,29,236,27,465,130,111,234,28,466,131,112,25,463,238,128,109,239,26,464,126,110,24,462,237,127,108,458,233,35,120,119,456,231,33,121,117,457,232,34,122,118,229,461,31,123,115,230,459,32,124,116,228,460,30,125,114,689,690,691,692,532,261,510,147,516,533,517,262,511,148,531,518,263,512,149,519,260,528,513,146,529,520,258,514,144,521,259,530,515,145,252,538,522,508,153,253,539,523,509,154,254,537,524,507,155,534,255,525,504,152,535,256,526,505,150,536,257,527,506,151,697,698,700,699,608,217,635,617,211,606,212,218,633,615,607,210,216,634,616,214,220,611,631,613,609,215,221,632,614,213,219,610,630,612,223,603,209,626,623,224,604,207,624,621,222,605,208,625,622,602,226,205,629,619,600,227,206,627,620,601,225,204,628,618,661,662,664,663,366,36,167,374,169,367,170,37,165,372,368,168,38,166,373,172,39,369,163,377,370,173,40,164,375,171,41,371,162,376,42,364,175,158,380,43,365,176,156,378,44,363,174,157,379,360,45,178,161,383,361,46,179,159,381,362,47,177,160,382,682,681,684,683,270,547,287,276,268,271,269,548,285,277,272,267,546,286,278,264,550,273,283,279,274,265,551,284,280,266,549,275,282,281,545,641,640,643,642,543,645,644,647,646,544,637,636,638,639,653,541,652,655,654,657,542,656,659,658,648,540,649,651,650,693,694,696,695,137,248,480,475,495,135,496,246,481,476,136,497,247,482,474,494,251,133,483,478,134,492,249,484,479,493,250,132,485,477,243,143,501,486,473,244,141,502,487,471,245,142,503,488,472,139,242,500,489,469,140,240,498,490,470,138,241,499,491,468,666,665,668,667,180,49,77,195,390,181,391,50,75,196,182,392,48,76,197,393,52,183,73,194,184,394,53,74,192,395,51,185,72,193,55,186,388,83,201,56,187,389,81,202,54,188,387,82,203,189,58,384,79,200,190,59,385,80,198,191,57,386,78,199,674,673,676,675 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#07e8f68f5124a8e3a0938e8678de1c72ed7349b338061e203d5db711c48e18fa, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 15:10:41 · history