Equation 677 Database

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Magma 51bfdda218a3…

magma 51bfdda218a3
Size
705
Isomorphism class hash
51bfdda218a39ad1393add7c1c64bfa174e67e7697f69b17b9e0d34a64c99731
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 18:18:03
Display reorder
660,72,297,276,92,194,73,298,277,90,192,74,299,278,91,193,296,71,279,88,197,294,69,280,89,195,295,70,281,87,196,78,303,274,83,189,79,304,275,81,190,80,305,273,82,191,302,77,270,86,188,300,75,271,84,186,301,76,272,85,187,663,669,672,668,247,112,479,138,244,248,113,477,139,245,246,111,478,140,243,108,250,475,141,240,109,251,476,142,241,110,249,474,143,242,253,103,485,144,235,254,104,483,145,236,252,102,484,146,234,106,256,481,147,238,107,257,482,148,239,105,255,480,149,237,685,688,691,689,158,329,198,587,455,156,327,199,585,453,157,328,200,586,454,325,161,201,583,451,326,159,202,584,452,324,160,203,582,450,153,320,204,593,461,154,318,205,591,459,155,319,206,592,460,323,152,207,589,457,321,150,208,590,458,322,151,209,588,456,665,662,664,670,58,266,575,419,121,59,264,573,417,122,57,265,574,418,120,269,61,571,415,124,267,62,572,416,125,268,60,570,414,123,64,261,581,425,119,65,262,579,423,117,63,263,580,424,118,260,67,577,421,115,258,68,578,422,116,259,66,576,420,114,676,681,678,674,629,137,551,527,395,627,135,549,525,393,628,136,550,526,394,133,625,547,523,391,134,626,548,524,392,132,624,546,522,390,635,128,557,533,401,633,126,555,531,399,634,127,556,532,400,131,631,553,529,397,129,632,554,530,398,130,630,552,528,396,671,667,661,666,467,313,371,361,407,465,314,369,362,405,466,312,370,360,406,316,463,367,364,403,317,464,368,365,404,315,462,366,363,402,473,311,377,359,413,471,309,375,357,411,472,310,376,358,412,307,469,373,355,409,308,470,374,356,410,306,468,372,354,408,697,695,696,694,598,15,620,99,41,599,16,618,100,39,597,17,619,101,40,14,594,616,98,44,12,595,617,96,42,13,596,615,97,43,656,21,659,658,657,651,22,650,649,648,652,23,655,654,653,20,600,622,93,38,18,601,623,94,36,19,602,621,95,37,702,704,701,703,491,221,25,56,608,489,219,26,54,606,490,220,24,55,607,217,487,28,52,604,218,488,29,53,605,216,486,27,51,603,497,212,31,47,614,495,210,32,45,612,496,211,30,46,613,215,493,34,50,610,213,494,35,48,611,214,492,33,49,609,698,700,699,693,503,174,285,352,443,501,175,286,353,441,502,176,287,351,442,177,499,284,348,439,178,500,282,349,440,179,498,283,350,438,509,180,291,343,449,507,181,292,344,447,508,182,293,342,448,183,505,290,346,445,184,506,288,347,446,185,504,289,345,444,677,673,675,684,563,5,641,230,539,561,3,639,228,537,562,4,640,229,538,0,559,637,233,535,2,560,638,231,536,1,558,636,232,534,569,11,647,225,545,567,9,645,226,543,568,10,646,227,544,7,565,643,224,541,8,566,644,222,542,6,564,642,223,540,680,683,679,682,431,166,383,338,515,429,167,381,336,513,430,165,382,337,514,162,427,379,341,511,163,428,380,339,512,164,426,378,340,510,437,172,389,333,521,435,173,387,334,519,436,171,388,335,520,168,433,385,332,517,169,434,386,330,518,170,432,384,331,516,687,686,690,692 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#7662547f1ab019fdebb7f412cf128566d4c1d6f1fe751ad78d224fe85422d2cf, 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 18:18:04 · history