Equation 677 Database

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Magma ec47054e8373…

magma ec47054e8373
Size
705
Isomorphism class hash
ec47054e8373509829c030d7447b00171311edae218747b0f52a3398cf5c208a
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 15:03:26
Display reorder
660,256,590,265,243,231,257,588,266,244,232,255,589,264,245,233,252,593,268,242,230,253,591,269,240,228,592,254,267,241,229,271,262,596,249,237,272,263,594,250,238,270,261,595,251,239,258,274,599,248,236,259,275,597,246,234,260,273,598,247,235,687,688,686,685,442,304,451,433,180,443,305,452,434,181,441,303,450,432,182,438,300,454,436,183,439,301,455,437,184,302,440,453,435,185,457,448,310,431,186,458,449,311,429,187,456,447,309,430,188,444,460,306,427,189,445,461,307,428,190,446,459,308,426,191,703,704,701,702,398,583,227,122,112,396,584,225,120,113,397,582,226,121,111,401,586,223,125,108,399,587,224,123,109,585,400,222,124,110,218,393,581,128,118,216,394,579,126,119,217,395,580,127,117,392,221,577,131,114,390,219,578,129,115,391,220,576,130,116,671,672,670,669,469,199,313,336,325,470,200,314,337,326,468,198,312,338,324,472,202,316,339,328,473,203,317,340,329,201,471,315,341,327,319,467,197,342,331,320,465,195,343,332,318,466,196,344,330,463,322,193,345,334,464,323,194,346,335,462,321,192,347,333,679,680,678,677,521,352,482,509,486,519,353,480,507,487,520,351,481,508,488,517,348,485,505,489,518,349,483,506,490,350,516,484,504,491,477,512,358,500,492,478,510,359,498,493,479,511,357,499,494,515,476,354,503,495,513,474,355,501,496,514,475,356,502,497,692,691,690,689,92,144,0,377,552,90,145,2,375,553,91,146,1,376,554,95,147,4,373,555,93,148,5,374,556,149,94,3,372,557,7,87,150,383,550,8,88,151,381,551,6,89,152,382,549,86,10,153,379,546,84,11,154,380,547,85,9,155,378,548,699,700,698,697,69,13,25,59,36,70,14,26,57,37,71,12,24,58,38,68,16,28,55,39,66,17,29,56,40,15,67,27,54,41,31,60,19,50,42,32,61,20,48,43,30,62,18,49,44,63,34,22,53,45,64,35,23,51,46,65,33,21,52,47,663,664,662,661,616,276,626,606,163,617,277,624,607,164,615,278,625,608,162,612,279,629,609,166,613,280,627,610,167,281,614,628,611,165,632,622,282,604,161,630,623,283,605,159,631,621,284,603,160,618,635,285,600,157,619,633,286,601,158,620,634,287,602,156,682,683,684,681,649,105,651,650,648,653,106,655,654,652,656,107,659,658,657,644,104,647,646,645,637,102,638,636,639,103,641,643,642,640,571,565,96,563,386,572,566,97,561,384,570,564,98,562,385,568,574,99,559,389,569,575,100,560,387,567,573,101,558,388,695,696,693,694,528,215,538,368,80,529,213,539,366,78,530,214,537,367,79,531,211,534,371,83,532,212,535,369,81,210,533,536,370,82,544,526,206,363,75,545,527,204,364,76,543,525,205,365,77,522,540,209,362,74,523,541,207,360,72,524,542,208,361,73,667,668,665,666,142,169,410,288,416,143,170,408,289,414,141,168,409,290,415,138,172,413,291,419,139,173,411,292,417,171,140,412,293,418,405,133,175,294,422,406,134,176,295,420,407,132,174,296,421,136,404,178,297,425,137,402,179,298,423,135,403,177,299,424,675,676,673,674 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#01253a2afae29ad04ad4e5938d81c583acd3aeb3895dbf3461a9c0b97e71e908, 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 15:03:27 · history