Equation 677 Database

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Magma 5b957e0c215c…

magma 5b957e0c215c
Size
705
Isomorphism class hash
5b957e0c215c48a00273121f821ad1043a08776244e1b14c9a6f2e0ee3b16eb3
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 16:25:27
Display reorder
704,15,535,520,509,16,536,521,507,534,17,519,508,14,538,516,505,12,539,517,506,13,537,518,504,21,533,526,515,22,531,527,513,23,532,525,514,20,529,522,511,18,530,523,512,19,528,524,510,540,541,542,543,544,545,546,547,551,549,550,548,660,663,661,662,144,316,354,344,145,317,355,342,315,146,356,343,147,312,357,347,148,313,358,345,149,314,359,346,150,322,352,339,151,323,353,340,152,321,351,341,153,318,348,338,154,319,349,336,155,320,350,337,332,330,331,335,333,334,327,328,325,326,324,329,691,689,690,688,47,561,591,581,45,562,592,579,563,46,593,580,43,560,590,577,44,558,588,578,42,559,589,576,38,552,597,587,36,553,598,585,37,554,599,586,41,555,596,583,39,556,594,584,40,557,595,582,569,567,568,565,566,564,575,573,570,571,572,574,671,669,670,668,48,364,402,392,49,365,403,390,363,50,404,391,51,360,405,395,52,361,406,393,53,362,407,394,54,370,400,387,55,371,401,388,56,369,399,389,57,366,396,386,58,367,397,384,59,368,398,385,380,378,379,383,381,382,375,376,373,374,372,377,678,677,679,676,3,183,179,210,4,184,177,211,185,5,178,212,2,182,175,213,1,180,176,214,0,181,174,215,9,189,170,208,10,190,168,209,11,191,169,207,8,188,173,204,6,186,171,205,7,187,172,206,199,200,198,202,203,201,197,195,192,193,194,196,666,665,667,664,657,658,659,656,649,648,650,651,654,652,655,653,641,642,643,640,645,646,647,644,636,638,639,637,621,622,623,620,613,614,615,612,617,618,619,616,632,634,635,633,625,626,627,624,628,630,631,629,26,24,25,29,27,28,32,30,34,35,33,31,692,694,693,695,64,108,102,90,65,109,103,91,110,63,104,92,60,111,105,93,61,112,106,94,62,113,107,95,70,114,100,88,71,115,101,89,69,116,99,87,66,117,96,84,67,118,97,85,68,119,98,86,78,79,80,81,82,83,76,77,74,72,73,75,700,702,701,703,130,242,234,223,131,240,235,224,241,129,236,222,126,245,237,226,127,243,238,227,128,244,239,225,121,248,232,221,122,246,233,219,120,247,231,220,124,251,228,217,125,249,229,218,123,250,230,216,263,261,262,259,260,258,254,252,256,257,255,253,696,698,697,699,161,503,481,470,159,501,482,468,502,160,480,469,157,499,484,473,158,500,485,471,156,498,483,472,167,494,487,476,165,492,488,474,166,493,486,475,163,497,490,479,164,495,491,477,162,496,489,478,458,456,457,461,459,460,464,462,466,467,465,463,675,673,674,672,134,272,302,288,132,270,300,289,271,133,301,290,137,275,305,291,135,273,303,292,136,274,304,293,140,267,308,294,138,268,306,295,139,269,307,296,143,266,311,297,141,264,309,298,142,265,310,299,277,278,276,280,281,279,283,284,285,286,287,282,680,682,683,681,609,422,416,454,610,420,414,455,421,611,415,453,608,425,419,450,606,423,417,451,607,424,418,452,600,428,411,445,601,426,412,446,602,427,413,444,603,431,410,448,604,429,408,449,605,430,409,447,443,441,442,439,440,438,434,432,436,437,435,433,684,687,685,686 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#3180ad8dfd10ba7152583c35a71774bceecf2852df6e850dd8c0dada693f6036, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:25:28 · history