Equation 677 Database

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Magma 84dfb0bb1e54…

magma 84dfb0bb1e54
Size
705
Isomorphism class hash
84dfb0bb1e541c5719c2fd2870bbeedd8484bcf6f718e19b18f3ae474beebde1
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 15:03:52
Display reorder
660,614,34,601,618,604,634,35,621,638,624,654,33,640,658,644,594,30,580,598,584,554,31,541,558,544,32,574,561,578,564,420,434,25,438,424,441,453,26,456,444,461,474,24,478,464,494,481,28,498,484,514,501,29,518,504,534,520,27,538,524,689,693,697,692,613,16,608,610,609,633,17,628,630,629,653,15,648,650,649,593,12,588,590,589,553,13,548,550,549,14,573,568,570,569,428,433,22,430,429,448,452,23,450,449,468,473,21,470,469,493,488,18,490,489,513,508,19,510,509,533,528,20,530,529,691,698,699,688,43,113,52,150,405,44,111,53,151,406,42,112,51,152,407,46,109,48,153,404,47,110,49,154,402,108,45,50,155,403,58,41,119,148,396,59,39,117,149,397,57,40,118,147,398,37,54,115,144,399,38,55,116,145,400,36,56,114,146,401,666,680,678,665,89,5,345,218,229,87,3,346,216,230,88,4,347,217,228,85,0,344,221,232,86,2,342,219,233,1,84,343,220,231,336,95,11,224,235,337,93,9,222,236,338,94,10,223,234,91,339,7,227,238,92,340,8,225,239,90,341,6,226,237,671,675,673,668,602,198,600,612,617,622,199,620,632,637,642,200,641,652,657,582,201,581,592,597,542,202,540,552,557,203,562,560,572,577,421,422,196,432,437,442,457,197,458,459,460,462,195,472,477,482,480,192,492,497,502,500,193,512,517,522,521,194,532,537,700,687,703,702,605,75,619,607,603,625,76,639,627,623,645,77,659,647,643,585,74,599,587,583,545,72,559,547,543,73,565,579,567,563,439,425,81,427,423,440,445,82,447,443,479,465,83,467,463,485,499,80,487,483,505,519,78,507,503,525,539,79,527,523,704,686,690,701,616,172,615,606,611,636,173,635,626,631,656,171,655,646,651,596,168,595,586,591,556,169,555,546,551,170,576,575,566,571,435,436,178,426,431,454,455,179,446,451,475,476,177,466,471,496,495,174,486,491,516,515,175,506,511,536,535,176,526,531,695,694,685,696,297,105,205,266,417,298,106,206,264,418,299,107,204,265,419,296,104,208,269,416,294,102,209,267,414,103,295,207,268,415,211,288,96,272,408,212,289,97,270,409,210,290,98,271,410,291,214,99,275,411,292,215,100,273,412,293,213,101,274,413,681,684,662,663,121,60,134,333,357,122,61,132,334,358,120,62,133,335,359,124,63,137,332,356,125,64,135,330,354,65,123,136,331,355,140,127,66,324,348,138,128,67,325,349,139,126,68,326,350,130,143,69,327,351,131,141,70,328,352,129,142,71,329,353,672,674,683,669,285,247,261,369,393,286,248,262,370,394,287,246,263,371,395,284,250,260,368,392,282,251,258,366,390,249,283,259,367,391,252,276,245,360,384,253,277,243,361,385,254,278,244,362,386,279,255,241,363,387,280,256,242,364,388,281,257,240,365,389,676,679,667,661,167,184,321,309,381,165,185,322,310,382,166,183,323,311,383,163,180,320,308,380,164,181,318,306,378,182,162,319,307,379,312,158,190,300,372,313,156,191,301,373,314,157,189,302,374,161,315,186,303,375,159,316,187,304,376,160,317,188,305,377,664,677,670,682 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#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 15:03:54 · history