Equation 677 Database

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Magma 8bce9d7a215b…

magma 8bce9d7a215b
Size
705
Isomorphism class hash
8bce9d7a215b86c78457a49483737fc829e6a29f7b9b072f77f0cb12a2f4f19a
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 20:41:56
Display reorder
660,493,72,494,481,490,514,513,501,510,73,534,74,533,521,530,474,473,75,460,470,432,431,76,429,428,454,453,77,440,450,78,613,601,614,610,633,79,620,634,630,653,80,640,654,650,81,595,580,596,590,82,555,540,556,550,576,83,575,560,570,688,690,687,697,485,232,487,486,488,507,505,506,508,233,527,234,525,526,528,467,465,235,466,468,439,437,236,438,424,447,445,237,446,448,230,605,606,607,608,625,231,626,627,628,645,229,646,647,648,226,585,586,587,588,227,545,546,547,548,567,228,565,566,568,686,685,689,695,407,244,43,347,287,44,408,348,288,245,42,246,409,349,289,46,406,247,346,286,47,404,248,344,284,45,405,249,345,285,242,413,353,41,293,414,243,354,39,294,415,241,355,40,295,238,412,352,37,292,239,410,350,38,290,36,240,411,351,291,664,673,667,680,201,122,299,207,158,300,202,208,156,120,301,121,203,209,157,298,200,125,206,161,296,198,123,204,159,297,199,124,205,160,128,192,213,305,164,193,126,214,306,162,194,127,215,307,163,131,195,212,304,167,129,196,210,302,165,303,130,197,211,166,675,662,666,665,496,103,482,489,492,502,516,509,512,104,522,102,536,529,532,462,476,106,469,472,423,427,107,425,426,442,456,105,449,452,101,616,609,602,612,636,99,629,622,632,656,100,649,642,652,97,598,589,582,594,98,558,549,542,554,562,96,578,569,574,703,691,700,701,499,134,498,497,491,518,519,517,511,132,537,133,539,538,531,477,479,137,478,471,421,422,135,420,430,457,459,136,458,451,140,619,617,618,611,637,138,639,638,631,659,139,658,657,651,143,599,593,592,591,141,559,553,552,551,572,142,579,573,571,702,694,704,698,483,145,484,480,495,504,503,500,515,146,524,144,523,520,535,464,463,148,461,475,436,435,149,434,433,444,443,147,441,455,151,603,600,604,615,623,152,621,624,635,643,150,641,644,655,154,583,581,584,597,155,543,541,544,557,564,153,563,561,577,693,692,699,696,117,93,311,225,29,312,118,223,27,94,313,95,119,224,28,310,116,92,221,25,308,114,90,222,26,309,115,91,220,24,84,108,216,317,35,109,85,417,318,33,110,86,419,319,34,87,111,219,316,31,88,112,217,314,32,315,89,113,218,30,684,682,668,676,179,60,371,189,323,372,177,190,324,61,373,62,178,191,325,370,175,63,188,322,368,176,64,186,320,369,174,65,187,321,66,170,180,377,329,168,67,181,378,330,169,68,182,379,331,69,173,183,376,328,70,171,184,374,326,375,71,172,185,327,669,661,677,683,335,21,395,257,1,396,336,258,0,22,397,23,337,256,2,394,334,20,260,3,392,332,18,261,4,393,333,19,259,5,12,341,255,401,6,342,13,253,402,7,343,14,254,403,8,15,340,251,400,9,16,338,252,398,10,399,17,339,250,11,672,671,679,670,383,57,274,359,267,275,384,360,265,58,276,59,385,361,266,277,382,56,358,263,278,380,54,356,264,279,381,55,357,262,48,389,365,280,273,390,49,366,416,271,391,50,367,418,272,51,388,364,281,269,52,386,362,282,270,283,53,387,363,268,663,674,681,678 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#cc21ed90a723dc84f76676d15ec858e33ef625916c28841b110b43408fa38d16, 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 20:41:57 · history