Equation 677 Database

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Magma 5d533a749852…

magma 5d533a749852
Size
705
Isomorphism class hash
5d533a74985277d4381e1e6595d7acf120532d176cac17cb492156fc4b0078d8
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 15:23:37
Display reorder
660,338,324,280,106,214,336,281,107,215,325,337,326,279,105,213,323,334,283,102,217,321,335,284,103,218,322,333,282,104,216,278,344,330,97,220,342,331,98,276,221,343,332,96,277,219,329,340,100,274,223,327,341,101,275,224,328,339,99,273,222,666,672,661,665,56,575,193,458,445,54,194,456,446,573,55,574,192,457,444,571,59,189,454,441,572,57,190,455,442,570,58,191,453,443,199,51,581,464,451,52,579,462,200,452,53,580,463,198,450,577,50,460,195,447,578,48,461,196,448,576,49,459,197,449,687,685,691,689,506,3,248,303,482,504,246,304,480,4,505,5,247,305,481,2,502,244,306,478,1,503,245,307,479,0,501,243,308,477,239,512,9,301,488,510,10,302,237,486,511,11,300,238,487,8,508,297,242,484,6,509,298,240,485,7,507,299,241,483,669,667,668,662,71,548,13,547,422,69,14,543,420,544,70,546,12,545,421,539,67,16,540,418,541,68,17,542,419,538,66,15,537,417,19,62,560,559,428,60,555,556,20,426,61,557,558,18,427,551,65,552,22,424,554,63,553,23,425,549,64,550,21,423,680,676,679,681,434,629,74,530,410,432,72,528,408,627,433,628,73,529,409,625,430,77,526,406,626,431,75,527,407,624,429,76,525,405,80,440,635,536,416,438,633,534,78,414,439,634,535,79,415,631,436,532,83,412,632,437,533,81,413,630,435,531,82,411,670,663,664,671,110,386,232,294,494,108,233,295,492,384,109,385,231,296,493,382,113,235,293,490,383,111,236,291,491,381,112,234,292,489,230,116,392,285,500,114,390,286,228,498,115,391,287,229,499,388,119,288,226,496,389,117,289,227,497,387,118,290,225,495,695,696,693,694,619,599,133,566,124,620,134,564,125,597,618,598,132,565,123,595,615,129,562,120,596,616,130,563,121,594,617,131,561,122,139,659,658,656,657,651,650,648,140,649,655,654,652,138,653,601,621,568,135,126,602,622,569,136,127,600,623,567,137,128,702,701,704,703,148,89,25,587,608,149,26,585,606,87,147,88,24,586,607,85,151,28,583,604,86,152,29,584,605,84,150,27,582,603,31,146,95,593,614,144,93,591,32,612,145,94,592,30,613,91,142,589,34,610,92,143,590,35,611,90,141,588,33,609,697,699,700,698,470,270,201,374,361,468,202,372,362,271,469,272,203,373,360,269,466,204,370,357,267,467,205,371,358,268,465,206,369,359,207,476,261,380,367,474,262,378,208,368,475,263,379,209,366,264,472,376,210,363,265,473,377,211,364,266,471,375,212,365,675,674,677,684,177,176,38,163,641,178,36,164,639,174,179,175,37,162,640,172,180,41,159,637,173,181,39,160,638,171,182,40,161,636,44,183,167,154,647,184,165,155,42,645,185,166,153,43,646,170,186,157,47,643,168,187,158,45,644,169,188,156,46,642,682,683,673,678,518,398,313,351,257,516,314,352,255,396,517,397,312,353,256,394,514,309,354,260,395,515,310,355,258,393,513,311,356,259,319,524,404,349,252,522,402,350,320,253,523,403,348,318,254,400,520,345,315,251,401,521,346,316,249,399,519,347,317,250,692,690,688,686 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#164604ba66664ae7e7b126fe65d39300d84fb27e5ce614035873663e987c6567, 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 15:23:39 · history