Equation 677 Database

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Magma 9fa6b5ff4e7f…

magma 9fa6b5ff4e7f
Size
705
Isomorphism class hash
9fa6b5ff4e7f96eda5c966c2a5e9ceb1721f62f656eb9b10ae8b2ffb38db2866
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 21:21:59
Display reorder
660,32,222,411,68,471,409,220,33,69,469,34,410,70,221,470,407,35,225,71,467,408,36,223,72,468,406,37,224,73,466,30,66,402,228,462,31,67,400,226,460,29,65,401,227,461,62,26,405,231,465,63,27,403,229,463,64,28,404,230,464,670,663,666,671,399,141,319,435,255,320,142,397,433,253,398,321,434,140,254,318,395,137,431,251,316,396,138,432,252,317,394,139,430,250,390,426,325,132,246,388,424,326,133,244,389,425,327,131,245,429,393,324,135,249,427,391,322,136,247,428,392,323,134,248,688,689,686,687,507,279,540,459,483,538,277,505,457,481,506,539,458,278,482,536,503,275,455,479,537,504,276,456,480,535,502,274,454,478,498,450,531,270,474,496,448,529,268,472,497,449,530,269,473,453,501,534,273,477,451,499,532,271,475,452,500,533,272,476,665,669,667,668,365,359,152,339,447,153,360,366,337,445,364,154,338,358,446,151,368,362,335,443,149,369,363,336,444,150,367,361,334,442,371,330,143,357,438,372,328,144,355,436,370,329,145,356,437,333,374,146,353,441,331,375,147,354,439,332,373,148,352,440,676,673,675,679,240,384,621,423,351,619,382,238,421,349,239,620,422,383,350,617,243,387,419,347,618,241,385,420,348,616,242,386,418,346,235,414,612,379,342,236,412,610,380,340,237,413,611,381,341,417,234,615,378,345,415,232,613,376,343,416,233,614,377,344,664,672,661,662,213,263,564,202,597,562,264,211,203,595,212,563,204,262,596,560,209,266,205,593,561,210,267,206,594,559,208,265,207,592,219,200,555,261,588,217,201,553,259,586,218,199,554,260,587,196,215,558,257,591,197,216,556,258,589,198,214,557,256,590,694,696,697,693,656,89,657,659,658,651,90,650,649,648,652,653,655,91,654,1,514,88,104,583,0,515,86,105,584,2,516,87,106,585,509,99,7,95,578,510,100,8,96,579,508,98,6,97,577,102,512,3,94,581,103,513,4,92,582,101,511,5,93,580,704,703,702,701,188,127,39,646,647,40,125,189,643,642,187,38,645,126,644,42,184,130,638,639,43,185,128,640,641,41,186,129,637,636,194,182,45,122,12,195,183,46,123,10,193,181,44,124,11,634,190,48,121,635,179,191,49,119,13,180,192,47,120,9,699,695,700,698,303,57,495,552,633,493,58,301,550,631,302,494,551,56,632,491,299,60,548,629,492,300,61,549,630,490,298,59,547,628,294,543,486,55,624,292,541,484,53,622,293,542,485,54,623,546,297,489,51,627,544,295,487,52,625,545,296,488,50,626,680,677,684,674,81,304,576,609,528,574,305,82,607,526,80,575,608,306,527,572,84,307,605,524,573,85,308,606,525,571,83,309,604,523,79,600,567,310,519,77,598,565,311,517,78,599,566,312,518,603,75,570,313,522,601,76,568,314,520,602,74,569,315,521,682,681,678,683,288,22,112,171,162,110,20,286,172,163,287,111,170,21,161,108,291,25,167,165,109,289,23,168,166,107,290,24,169,164,283,177,118,17,160,284,178,116,18,158,285,176,117,19,159,173,282,114,16,156,174,280,115,14,157,175,281,113,15,155,690,691,685,692 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#eb741fb6db55479c3e56ca4f84f09a48d9f1cbf15ed347cc0747015cb842acab, 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 21:22:00 · history