Equation 677 Database

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Magma 199276c7e88e…

magma 199276c7e88e
Size
705
Isomorphism class hash
199276c7e88e97711a50f84c246e2930306078a58a5dec23ba2ff27755e27373
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 19:16:41
Display reorder
660,32,435,387,138,134,436,30,135,388,136,133,31,437,389,137,35,434,130,386,141,33,432,131,384,139,34,433,132,385,140,27,441,125,393,144,28,442,126,394,142,29,443,124,395,143,440,26,128,392,147,390,438,24,129,145,439,25,127,391,146,664,668,662,661,182,286,447,571,599,284,183,600,448,572,601,181,285,449,573,178,289,598,446,570,179,287,596,444,568,180,288,597,445,569,173,292,605,453,577,174,290,606,454,578,172,291,607,455,579,295,176,604,452,576,450,293,177,602,574,294,175,603,451,575,685,689,688,686,99,583,555,167,60,584,97,58,556,168,59,98,585,557,166,95,582,63,554,170,96,580,61,552,171,94,581,62,553,169,90,589,55,561,165,88,590,56,562,163,89,591,57,563,164,588,93,54,560,161,558,586,91,52,162,587,92,53,559,160,671,667,665,669,230,66,302,196,194,64,231,195,303,197,193,232,65,304,198,233,69,190,305,199,234,67,191,306,200,235,68,192,307,201,228,72,185,300,202,229,70,186,301,203,227,71,184,299,204,75,224,188,296,205,297,73,225,189,206,74,226,187,298,207,673,682,676,683,246,495,423,323,317,496,247,318,424,324,319,245,497,425,325,242,494,316,422,322,243,492,314,420,320,244,493,315,421,321,237,501,308,429,329,238,502,309,430,330,236,503,310,431,331,500,240,311,428,328,426,498,241,312,326,499,239,313,427,327,666,672,670,663,156,459,507,531,411,460,154,412,508,532,413,155,461,509,533,159,458,410,506,530,157,456,408,504,528,158,457,409,505,529,151,465,417,513,537,152,466,418,514,538,153,467,419,515,539,464,150,416,512,536,510,462,148,414,534,463,149,415,511,535,695,694,698,696,217,567,595,211,48,631,215,630,628,629,632,216,633,634,635,213,566,51,592,210,214,564,49,593,208,212,565,50,594,209,223,649,648,650,651,221,653,652,654,655,222,657,656,658,659,644,219,645,646,647,638,636,220,637,639,640,218,641,642,643,701,702,704,703,114,334,250,345,261,335,112,262,248,346,260,113,336,249,347,117,337,264,253,344,115,338,265,251,342,116,339,263,252,343,120,622,267,256,623,118,625,268,254,624,119,627,266,255,626,620,123,270,259,621,257,332,121,271,340,333,122,269,258,341,699,693,700,697,377,471,543,611,519,472,375,520,544,612,521,376,473,545,613,373,470,518,542,610,374,468,516,540,608,372,469,517,541,609,383,477,525,549,617,381,478,526,550,618,382,479,527,551,619,476,379,524,548,616,546,474,380,522,614,475,378,523,547,615,677,680,684,681,272,363,483,359,399,364,273,400,484,357,401,274,365,485,358,275,362,398,482,355,276,360,396,480,356,277,361,397,481,354,278,369,405,489,350,279,370,406,490,348,280,371,407,491,349,368,281,404,488,353,486,366,282,402,351,367,283,403,487,352,674,675,679,678,45,1,84,106,16,0,46,13,82,107,15,47,2,83,108,44,7,22,87,109,42,8,19,85,110,43,11,21,86,111,36,12,3,79,104,37,14,9,80,105,38,17,10,81,103,18,39,4,78,100,76,20,40,5,101,23,41,6,77,102,690,691,687,692 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#96b025dbf47c4a59dfaaf1b34262061bd74b6a84a8a9978c39bcd4e78b704a7c, 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 19:16:42 · history