Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 3db6b877687c…

magma 3db6b877687c
Size
705
Isomorphism class hash
3db6b877687c4793dbd2fde95ae144fb151c8e407bf365330f450214cdca4d75
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 21:50:17
Display reorder
660,208,207,209,206,204,205,213,214,215,212,210,211,415,416,414,418,419,417,413,411,412,409,410,408,342,343,344,345,346,347,340,341,339,336,337,338,558,559,560,561,562,563,556,557,555,552,553,554,224,222,223,227,225,226,219,220,221,218,216,217,677,682,680,688,588,590,589,593,591,592,596,594,595,599,597,598,190,191,189,186,187,188,181,182,180,184,185,183,449,447,448,445,446,444,455,453,454,451,452,450,256,257,255,252,253,254,262,263,261,258,259,260,69,70,71,68,66,67,60,61,62,63,64,65,690,701,694,697,388,387,389,386,384,385,393,394,395,392,390,391,372,373,374,375,376,377,378,379,380,381,382,383,541,542,540,544,545,543,547,548,546,550,551,549,329,327,328,325,326,324,335,333,334,331,332,330,404,402,403,407,405,406,399,400,401,398,396,397,664,669,670,676,194,193,192,196,197,195,199,200,198,202,203,201,275,273,274,271,272,270,266,264,265,269,267,268,465,466,467,464,462,463,456,457,458,459,460,461,80,78,79,83,81,82,75,76,77,74,72,73,600,601,602,603,604,605,606,607,608,609,610,611,678,685,683,687,472,471,473,470,468,469,477,478,479,476,474,475,623,621,622,619,620,618,614,612,613,617,615,616,281,279,280,277,278,276,287,285,286,283,284,282,15,16,17,14,12,13,21,22,23,20,18,19,85,86,84,88,89,87,91,92,90,94,95,93,692,702,703,699,640,639,641,638,636,637,645,646,647,644,642,643,5,3,4,0,2,1,11,9,10,7,8,6,505,506,504,508,509,507,511,512,510,514,515,513,302,300,301,305,303,304,308,306,307,311,309,310,108,109,110,111,112,113,114,115,116,117,118,119,689,696,695,698,152,151,150,154,155,153,149,147,148,145,146,144,106,107,105,102,103,104,97,98,96,100,101,99,160,161,159,156,157,158,166,167,165,162,163,164,137,135,136,133,134,132,143,141,142,139,140,138,39,40,41,38,36,37,45,46,47,44,42,43,661,662,663,667,170,169,168,172,173,171,175,176,174,178,179,177,423,424,425,422,420,421,429,430,431,428,426,427,239,237,238,235,236,234,230,228,229,233,231,232,566,564,565,569,567,568,572,570,571,575,573,574,348,349,350,351,352,353,354,355,356,357,358,359,679,681,684,686,537,539,538,535,536,534,530,528,529,533,531,532,526,527,525,522,523,524,517,518,516,520,521,519,125,123,124,121,122,120,131,129,130,127,128,126,315,316,317,314,312,313,321,322,323,320,318,319,648,649,650,651,652,653,654,655,656,657,658,659,691,700,693,704,298,297,299,296,294,295,288,289,290,291,292,293,501,502,503,500,498,499,492,493,494,495,496,497,35,33,34,31,32,30,26,24,25,29,27,28,490,491,489,486,487,488,481,482,480,484,485,483,625,626,624,628,629,627,631,632,630,634,635,633,665,668,672,675,251,250,249,246,247,248,241,242,240,244,245,243,438,439,440,441,442,443,436,437,435,432,433,434,361,362,360,364,365,363,367,368,366,370,371,369,52,53,51,48,49,50,58,59,57,54,55,56,579,580,581,578,576,577,585,586,587,584,582,583,666,671,673,674 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#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 21:50:18 · history