Equation 677 Database

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Magma 17005d0fc683…

magma 17005d0fc683
Size
705
Isomorphism class hash
17005d0fc683730fb740e763d873745ee916fb26e828673e8ad7af89deb67179
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 17:24:56
Display reorder
660,72,202,46,563,33,73,47,564,203,34,74,201,48,565,35,205,75,45,562,32,206,76,43,560,30,204,77,44,561,31,52,200,554,70,24,53,198,555,71,25,54,199,556,69,26,196,51,557,66,27,197,49,558,67,28,195,50,559,68,29,666,661,672,669,19,306,407,611,365,20,408,612,307,366,18,308,409,613,367,305,22,406,610,364,303,23,404,608,362,304,21,405,609,363,398,312,602,17,371,399,313,603,15,372,400,314,604,16,373,311,401,605,13,370,309,402,606,14,368,310,403,607,12,369,686,690,685,688,78,230,395,599,491,79,396,600,228,492,80,229,397,601,493,226,81,394,598,490,227,82,392,596,488,225,83,393,597,489,386,221,590,84,482,387,219,591,85,483,388,220,592,86,484,224,389,593,87,485,222,390,594,88,486,223,391,595,89,487,663,665,667,670,134,455,319,383,328,135,320,384,456,327,136,457,318,385,518,454,137,315,382,329,452,138,316,380,330,453,139,317,381,331,325,446,374,140,332,326,447,375,141,333,324,448,376,142,334,449,321,377,143,335,450,322,378,144,336,451,323,379,145,337,673,679,676,674,126,146,347,467,623,127,348,468,147,624,125,148,349,469,625,149,122,346,466,622,150,123,344,464,620,151,124,345,465,621,338,152,458,132,614,339,153,459,133,615,340,154,460,131,616,155,341,461,128,617,156,342,462,129,618,157,343,463,130,619,662,671,668,664,217,575,427,503,443,218,425,504,576,444,216,577,426,505,445,574,213,423,502,442,572,214,424,500,440,573,215,422,501,441,433,566,494,208,434,431,567,495,209,435,432,568,496,207,436,569,429,497,211,437,570,430,498,212,438,571,428,499,210,439,693,694,698,695,120,103,541,90,647,121,655,654,653,652,119,659,657,656,658,102,116,540,93,644,100,117,538,91,645,101,118,539,92,646,532,109,97,111,639,533,107,98,112,640,534,108,99,110,638,105,535,96,114,642,106,536,94,115,643,104,537,95,113,641,701,702,704,703,6,551,36,515,164,7,648,516,552,649,8,553,651,517,650,550,9,169,514,167,548,10,170,512,165,549,11,168,513,166,42,542,506,4,162,40,543,507,5,163,41,544,508,3,161,545,38,509,1,158,546,39,510,0,159,547,37,511,2,160,699,700,697,696,186,286,419,291,55,187,420,292,287,56,188,285,421,293,519,289,185,418,294,58,290,183,416,295,59,288,184,417,296,57,410,284,297,192,61,411,282,298,193,62,412,283,299,194,60,280,413,300,191,64,281,414,301,189,65,279,415,302,190,63,675,678,684,681,353,587,635,479,529,354,636,480,588,530,355,589,637,481,531,586,352,634,478,528,584,350,632,476,526,585,351,633,477,527,626,578,470,359,520,627,579,471,360,521,628,580,472,361,522,581,629,473,358,523,582,630,474,356,524,583,631,475,357,525,683,680,682,677,182,259,238,268,243,180,239,269,260,244,181,258,237,267,245,255,178,241,271,246,256,179,242,272,247,257,177,240,270,248,236,265,274,173,249,234,266,275,171,250,235,264,273,172,251,261,232,277,176,252,262,233,278,174,253,263,231,276,175,254,687,689,691,692 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#520f0c8ba72cb86fc7f95b2cd25444b775e13567ed9a2b839438811596de084e, 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 17:24:57 · history