Equation 677 Database

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Magma 0067847b0977…

magma 0067847b0977
Size
705
Isomorphism class hash
0067847b0977df93ae1e5882e974291f51a6c56c7a42ef21469e9c8b51778902
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 17:23:02
Display reorder
660,83,377,476,19,416,81,375,474,20,414,82,376,475,18,415,373,79,479,22,419,374,80,23,417,477,21,372,78,478,418,89,368,482,17,422,87,366,480,15,420,88,367,481,16,421,371,85,485,13,425,369,86,483,14,423,370,84,484,12,424,664,667,663,662,211,276,189,180,208,212,277,190,181,209,210,278,191,182,207,279,214,188,183,204,280,215,184,205,186,185,281,213,187,206,217,274,195,178,199,218,275,196,179,200,216,273,197,177,198,270,220,194,174,202,271,221,192,175,203,272,219,193,176,201,690,688,692,686,524,67,64,440,542,522,68,65,438,540,523,66,63,439,541,70,527,60,443,545,71,525,441,543,61,442,69,526,62,544,530,73,55,446,548,528,74,56,444,546,529,72,54,445,547,76,533,58,449,551,77,531,59,447,549,75,532,57,448,550,669,671,670,665,428,227,283,452,97,426,225,284,450,98,427,226,282,451,96,223,431,286,455,100,224,429,453,101,287,454,222,430,285,99,434,233,289,458,95,432,231,290,456,93,433,232,288,457,94,229,437,292,461,91,230,435,293,459,92,228,436,291,460,90,674,680,675,676,335,245,311,300,323,333,243,309,301,321,334,244,310,302,322,241,331,307,303,319,242,332,304,320,308,305,240,330,306,318,341,236,317,298,329,339,234,315,299,327,340,235,316,297,328,239,337,313,294,325,237,338,314,295,326,238,336,312,296,324,661,672,668,666,464,122,35,380,512,462,120,33,378,510,463,121,34,379,511,125,467,31,383,515,123,465,381,513,32,382,124,466,30,514,470,117,26,386,518,468,118,24,384,516,469,119,25,385,517,116,473,29,389,521,114,471,27,387,519,115,472,28,388,520,695,693,696,694,37,562,568,538,572,38,563,569,539,570,36,561,567,537,571,558,40,564,534,575,559,41,535,573,565,536,560,39,566,574,644,553,645,646,647,639,554,637,636,638,640,552,641,642,643,556,657,658,656,659,557,648,650,649,651,555,652,654,653,655,703,701,704,702,248,148,134,152,578,246,149,132,150,576,247,147,133,151,577,144,251,137,155,581,145,249,153,579,135,154,146,250,136,580,254,139,129,158,584,252,140,130,156,582,253,138,131,157,583,142,257,128,161,587,143,255,126,159,585,141,256,127,160,586,697,700,698,699,8,412,359,348,111,6,413,357,349,112,7,411,358,350,113,408,11,355,351,110,409,9,352,108,356,353,410,10,354,109,3,403,365,346,102,4,404,363,347,103,5,402,364,345,104,406,2,361,342,105,407,1,362,343,106,405,0,360,344,107,677,679,682,684,488,259,626,602,168,486,260,624,600,169,487,258,625,601,170,262,491,629,605,171,263,489,603,172,627,604,261,490,628,173,494,265,632,608,166,492,266,630,606,167,493,264,631,607,165,268,497,635,611,162,269,495,633,609,163,267,496,634,610,164,678,683,673,681,614,47,590,398,500,612,45,588,396,498,613,46,589,397,499,43,617,593,401,503,44,615,399,501,591,400,42,616,592,502,620,53,596,393,506,618,51,594,394,504,619,52,595,395,505,49,623,599,392,509,50,621,597,390,507,48,622,598,391,508,691,689,687,685 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#514dffc0e0e0286a01e02cffb6912c439b28b51da818e57a2690264fae383974, 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 17:23:03 · history