Equation 677 Database

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Magma 55cb0c844731…

magma 55cb0c844731
Size
705
Isomorphism class hash
55cb0c8447317b67e2e8f9727b427f5962863da11a77934bc6c1f6bf7d69fe7e
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 18:22:48
Display reorder
660,28,308,84,286,293,306,287,29,85,291,307,285,27,86,292,304,24,87,289,296,305,25,88,290,294,303,26,89,288,295,34,90,314,284,299,35,91,312,282,297,33,92,313,283,298,93,30,310,280,302,94,31,311,281,300,95,32,309,279,301,685,686,688,687,159,382,389,402,119,383,403,160,387,117,381,404,161,388,118,385,158,392,401,115,386,156,390,399,116,384,157,391,400,114,165,395,380,408,110,166,393,378,409,108,167,394,379,410,109,398,164,376,407,113,396,162,377,405,111,397,163,375,406,112,701,702,704,703,277,567,580,79,558,568,80,278,581,559,569,78,276,579,560,566,273,576,82,561,564,274,577,83,562,565,275,578,81,563,268,586,573,77,556,269,587,574,75,557,267,585,575,76,555,582,271,572,73,552,583,272,570,74,553,584,270,571,72,554,670,669,672,671,171,422,433,445,457,420,446,172,434,458,421,444,173,432,456,418,170,429,441,453,419,168,430,442,454,417,169,431,443,455,177,424,413,436,448,178,425,411,437,449,179,423,412,435,447,427,176,416,439,451,428,174,414,440,452,426,175,415,438,450,680,677,679,678,155,506,465,476,493,504,474,153,466,494,505,475,154,467,492,502,151,468,472,489,503,152,469,473,490,501,150,470,471,491,146,463,497,482,484,144,464,495,480,485,145,462,496,481,483,459,149,500,478,487,460,147,498,479,488,461,148,499,477,486,689,690,691,692,61,207,221,239,539,208,237,62,219,537,209,238,60,220,538,206,64,217,235,542,204,65,218,236,540,205,63,216,234,541,67,227,213,230,534,68,225,214,228,535,66,226,215,229,536,223,70,212,233,533,224,71,210,231,531,222,69,211,232,532,697,698,700,699,591,634,647,603,617,635,604,592,645,615,633,605,593,646,616,630,590,643,602,613,631,588,644,600,614,632,589,642,601,612,597,638,625,609,623,598,636,626,610,621,599,637,624,611,622,641,596,628,608,619,639,594,629,606,620,640,595,627,607,618,661,662,664,663,44,126,96,13,323,127,14,42,97,321,128,12,43,98,322,129,47,99,16,326,130,45,100,17,324,131,46,101,15,325,39,102,124,19,318,40,103,125,20,319,41,104,123,18,320,105,38,120,22,317,106,36,121,23,315,107,37,122,21,316,682,681,684,683,9,263,255,548,243,261,546,10,256,244,262,547,11,257,245,266,8,254,551,242,264,6,252,549,240,265,7,253,550,241,1,654,653,655,652,0,658,656,659,657,2,648,649,650,651,260,3,251,545,248,258,4,249,543,246,259,5,250,544,247,693,694,696,695,139,521,191,202,515,519,203,140,189,513,520,201,138,190,514,524,142,187,198,518,522,143,188,199,516,523,141,186,200,517,137,182,527,193,510,135,180,525,194,511,136,181,526,192,512,185,133,530,196,509,183,134,528,197,507,184,132,529,195,508,666,665,668,667,58,360,364,337,349,361,338,59,365,350,362,336,57,363,348,359,54,367,333,345,357,55,368,334,346,358,56,366,335,347,49,370,351,328,340,50,371,352,329,341,48,369,353,327,339,373,52,354,331,343,374,53,355,332,344,372,51,356,330,342,674,673,676,675 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#7eb365a46a73bc671c535e7eab37a7fd590c6d5c6b4c14d45f700003c9150a2d, 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 18:22:49 · history