Equation 677 Database

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Magma 8dbaa8eccd1f…

magma 8dbaa8eccd1f
Size
705
Isomorphism class hash
8dbaa8eccd1f9453d5e0ebc33ece1ed9e7135b4b2e162d59c5638f47f7fa93fa
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 21:50:39
Display reorder
660,242,241,240,244,245,243,247,248,246,250,251,249,423,424,425,422,420,421,429,430,431,428,426,427,302,300,301,305,303,304,308,306,307,311,309,310,22,23,21,18,19,20,13,14,12,16,17,15,364,365,363,360,361,362,370,371,369,366,367,368,673,681,689,678,657,659,658,655,656,654,650,648,649,653,651,652,508,509,507,504,505,506,514,515,513,510,511,512,534,535,536,537,538,539,532,533,531,528,529,530,449,447,448,445,446,444,455,453,454,451,452,450,599,597,598,595,596,594,590,588,589,593,591,592,661,665,674,667,322,321,323,320,318,319,312,313,314,315,316,317,261,262,263,260,258,259,252,253,254,255,256,257,437,435,436,433,434,432,443,441,442,439,440,438,211,212,210,214,215,213,209,207,208,205,206,204,378,379,380,381,382,383,376,377,375,372,373,374,672,677,690,679,131,130,129,126,127,128,121,122,120,124,125,123,76,77,75,72,73,74,82,83,81,78,79,80,108,109,110,111,112,113,114,115,116,117,118,119,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,695,704,703,701,145,144,146,147,148,149,150,151,152,153,154,155,622,623,621,618,619,620,613,614,612,616,617,615,479,477,478,475,476,474,470,468,469,473,471,472,28,29,27,24,25,26,34,35,33,30,31,32,559,560,558,562,563,561,557,555,556,553,554,552,684,696,697,691,185,184,183,180,181,182,190,191,189,186,187,188,399,400,401,398,396,397,405,406,407,404,402,403,342,343,344,345,346,347,340,341,339,336,337,338,231,232,233,230,228,229,237,238,239,236,234,235,281,279,280,277,278,276,287,285,286,283,284,282,663,664,675,669,626,625,624,628,629,627,631,632,630,634,635,633,46,47,45,42,43,44,37,38,36,40,41,39,167,165,166,163,164,162,158,156,157,161,159,160,486,487,488,489,490,491,484,485,483,480,481,482,566,564,565,569,567,568,572,570,571,575,573,574,685,692,698,693,60,62,61,65,63,64,68,66,67,71,69,70,325,326,324,328,329,327,331,332,330,334,335,333,387,388,389,386,384,385,393,394,395,392,390,391,226,227,225,222,223,224,217,218,216,220,221,219,272,270,271,275,273,274,267,268,269,266,264,265,671,686,688,683,8,7,6,10,11,9,5,3,4,0,2,1,497,495,496,493,494,492,503,501,502,499,500,498,585,586,587,584,582,583,576,577,578,579,580,581,177,178,179,176,174,175,168,169,170,171,172,173,640,641,639,636,637,638,646,647,645,642,643,644,694,700,702,699,605,604,603,600,601,602,610,611,609,606,607,608,140,138,139,143,141,142,135,136,137,134,132,133,544,545,543,540,541,542,550,551,549,546,547,548,524,522,523,527,525,526,519,520,521,518,516,517,459,460,461,458,456,457,465,466,467,464,462,463,662,666,676,668,293,292,291,288,289,290,298,299,297,294,295,296,348,349,350,351,352,353,354,355,356,357,358,359,54,55,56,57,58,59,52,53,51,48,49,50,199,200,198,202,203,201,197,195,196,193,194,192,408,409,410,411,412,413,414,415,416,417,418,419,670,680,687,682 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {64} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 21:50:40 · history