Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma fe1f5bd88bb2…

magma fe1f5bd88bb2
Size
705
Isomorphism class hash
fe1f5bd88bb29f6322793002467d6f5d91d5211c0c857c3309f72d7dbe16eeae
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 20:08:42
Display reorder
660,531,132,573,513,477,532,133,574,514,478,134,533,575,515,479,530,135,572,512,476,528,136,570,510,474,529,137,571,511,475,138,522,564,504,468,139,523,565,505,469,140,524,566,506,470,525,141,567,507,471,526,142,568,508,472,527,143,569,509,473,680,683,684,687,2,197,381,333,305,1,195,382,334,303,196,0,383,335,304,5,193,380,332,301,3,194,378,330,302,4,192,379,331,300,203,8,372,324,311,201,6,373,325,309,202,7,374,326,310,11,199,375,327,307,9,200,376,328,308,10,198,377,329,306,671,662,669,663,48,222,417,321,453,49,223,418,322,454,224,50,419,323,455,51,225,416,320,452,52,226,414,318,450,53,227,415,319,451,220,54,408,312,444,221,55,409,313,445,219,56,410,314,446,57,216,411,315,447,58,217,412,316,448,59,218,413,317,449,678,673,685,677,639,248,642,636,638,647,246,650,644,646,247,655,658,652,654,631,251,634,629,630,615,249,618,613,614,623,250,626,621,622,243,128,534,120,125,244,126,535,121,123,245,127,536,122,124,588,242,590,592,593,599,240,602,597,598,607,241,610,604,606,703,698,704,700,270,64,285,151,159,271,65,286,152,160,63,272,287,150,161,273,60,284,154,158,274,61,282,155,156,275,62,283,153,157,70,268,276,149,165,71,269,277,147,166,69,267,278,148,167,264,66,279,145,164,265,67,280,146,162,266,68,281,144,163,693,689,694,690,235,20,549,429,465,236,18,550,430,466,19,234,551,431,467,238,23,548,428,464,239,21,546,426,462,237,22,547,427,463,15,233,540,420,456,16,231,541,421,457,17,232,542,422,458,229,14,543,423,459,230,12,544,424,460,228,13,545,425,461,667,665,661,672,94,25,98,109,176,95,26,96,110,174,24,93,97,108,175,90,28,101,112,179,91,29,99,113,177,92,27,100,111,178,31,85,104,115,171,32,86,102,116,172,30,84,103,114,173,88,34,107,118,170,89,35,105,119,168,87,33,106,117,169,695,691,696,692,561,46,501,585,489,562,47,502,586,490,45,563,503,587,491,560,42,500,584,488,558,43,498,582,486,559,44,499,583,487,37,552,492,576,480,38,553,493,577,481,36,554,494,578,482,555,40,495,579,483,556,41,496,580,484,557,39,497,581,485,681,688,686,682,641,182,640,637,643,649,180,648,645,651,181,657,656,653,659,633,185,632,628,635,617,183,616,612,619,625,184,624,620,627,188,521,518,129,537,186,519,516,130,538,187,520,517,131,539,595,191,594,589,591,601,189,600,596,603,609,190,608,605,611,701,702,699,697,405,259,441,290,209,406,260,442,288,207,258,407,443,289,208,404,262,440,293,205,402,263,438,291,206,403,261,439,292,204,257,396,432,296,215,255,397,433,294,213,256,398,434,295,214,399,253,435,299,211,400,254,436,297,212,401,252,437,298,210,670,668,664,666,393,75,343,351,369,394,76,344,352,370,77,395,342,353,371,392,74,346,350,368,390,72,347,348,366,391,73,345,349,367,81,384,341,357,360,82,385,339,358,361,83,386,340,359,362,387,80,337,356,363,388,78,338,354,364,389,79,336,355,365,675,674,676,679 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#ba8e767ab0f178377cc5ca58de8baa4e7db92c571ba3737b1b055d153a9d0c2e, M = {60} 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 20:08:43 · history