Equation 677 Database

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Magma bdd2df3f6feb…

magma bdd2df3f6feb
Size
705
Isomorphism class hash
bdd2df3f6feb69f7f40bf237bfbdc2e29d1b2fcbe7403d9b31db6e52bbc0ee1c
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 20:38:52
Display reorder
660,614,128,607,604,606,126,624,634,627,626,127,644,654,647,646,131,584,594,587,586,129,544,554,547,546,130,564,574,567,566,427,434,424,123,426,446,452,443,124,445,467,474,464,125,466,494,487,484,122,486,514,507,504,120,506,534,527,524,121,526,688,687,686,697,608,68,611,602,615,66,622,628,631,635,67,642,648,651,655,71,582,588,591,595,69,542,548,551,555,70,562,568,571,575,431,428,422,63,435,450,447,441,64,453,471,468,462,65,475,488,491,482,62,495,508,511,502,60,515,528,531,522,61,535,694,704,700,689,274,55,260,405,194,56,406,275,258,192,54,407,273,259,193,58,404,270,263,197,59,402,271,261,195,57,403,272,262,196,255,265,396,53,200,256,266,397,51,198,257,264,398,52,199,268,254,399,49,203,269,252,400,50,201,267,253,401,48,202,674,669,676,680,145,170,232,161,321,168,159,146,233,322,169,160,144,231,323,173,157,148,228,320,171,158,149,229,318,172,156,147,230,319,238,151,167,176,312,239,152,165,174,313,237,150,166,175,314,154,234,163,179,315,155,235,164,177,316,153,236,162,178,317,666,664,684,678,601,38,600,613,603,36,633,620,621,623,37,653,640,641,643,41,593,581,580,583,39,553,540,541,543,40,573,561,560,563,420,421,433,44,423,442,457,459,42,458,461,460,473,43,463,480,481,493,47,483,501,500,513,45,503,521,520,533,46,523,692,685,698,702,610,222,619,612,617,223,632,630,639,637,224,652,650,659,657,225,592,590,599,597,226,552,550,559,557,227,572,570,579,577,439,430,432,220,437,440,449,451,221,455,479,470,472,219,477,490,499,492,216,497,510,519,512,217,517,530,539,532,218,537,696,701,695,691,618,283,605,609,616,284,629,638,625,636,282,649,658,645,656,286,589,598,585,596,287,549,558,545,556,285,569,578,565,576,425,438,429,281,436,444,456,448,279,454,465,478,469,280,476,498,485,489,277,496,518,505,509,278,516,538,525,529,276,536,693,699,690,703,357,190,345,333,250,191,334,358,346,251,189,335,359,347,249,186,332,356,344,246,187,330,354,342,247,188,331,355,343,248,336,348,324,181,241,337,349,325,182,242,338,350,326,180,240,351,339,327,184,244,352,340,328,185,245,353,341,329,183,243,667,679,665,670,206,133,369,288,309,134,289,204,370,310,132,290,205,371,311,136,291,209,368,308,137,292,207,366,306,135,293,208,367,307,360,212,294,139,300,361,210,295,140,301,362,211,296,138,302,215,363,297,142,303,213,364,298,143,304,214,365,299,141,305,672,663,682,661,393,2,417,109,93,1,110,394,418,94,0,108,395,419,95,5,112,392,416,92,3,113,390,414,90,4,111,391,415,91,408,384,115,8,84,409,385,116,6,85,410,386,114,7,86,387,411,118,11,87,388,412,119,9,88,389,413,117,10,89,681,662,671,675,381,27,19,80,103,28,78,382,20,104,29,79,383,18,102,26,83,380,22,106,24,81,378,23,107,25,82,379,21,105,17,372,75,33,101,15,373,76,34,99,16,374,77,35,100,375,13,74,32,97,376,14,72,30,98,377,12,73,31,96,683,677,668,673 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#c8b00e8ba82c54826bf93ef2b9b2d8eeb61b8eb7ac0797b661231f1bb38e050b, 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 20:38:53 · history