Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 7f2ed86e0f5b…

magma 7f2ed86e0f5b
Size
705
Isomorphism class hash
7f2ed86e0f5b05972f4baef6ae4ed7141e1bfcbb59f07a07a8b4b30a40f5aff3
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 19:20:15
Display reorder
660,282,64,289,262,255,283,65,260,287,256,261,63,281,288,254,60,278,285,265,258,61,279,286,263,259,62,280,284,264,257,273,70,295,268,253,274,71,293,266,251,272,69,294,267,252,276,66,291,271,249,277,67,292,269,250,275,68,290,270,248,685,686,688,687,431,9,398,421,414,432,10,419,399,415,420,7,433,400,413,0,430,401,417,410,2,428,402,418,411,5,429,403,416,412,437,1,396,427,405,438,3,397,425,406,439,4,395,426,404,436,6,392,423,408,434,8,393,424,409,435,11,394,422,407,701,702,704,703,583,236,595,619,607,581,237,617,593,605,618,238,582,594,606,239,579,591,615,603,240,580,592,616,604,241,578,590,614,602,574,242,586,610,598,572,243,584,608,596,573,244,585,609,597,577,245,589,613,601,575,246,587,611,599,576,247,588,612,600,670,669,672,671,144,440,155,132,164,142,441,130,156,165,131,442,143,154,163,443,140,151,128,167,444,141,152,129,168,445,139,153,127,166,150,446,161,138,170,148,447,162,136,171,149,448,160,137,169,146,449,157,134,173,147,450,158,135,174,145,451,159,133,172,680,677,679,678,475,57,486,454,491,473,58,452,487,492,453,59,474,485,493,56,471,482,457,490,54,472,483,455,488,55,470,484,456,489,466,48,477,460,497,464,49,478,458,498,465,50,476,459,499,469,51,480,463,496,467,52,481,461,494,468,53,479,462,495,689,690,691,692,102,552,119,195,20,103,553,193,117,18,194,551,104,118,19,548,105,115,198,23,549,106,116,196,21,550,107,114,197,22,100,558,110,190,15,101,559,108,191,16,99,557,109,192,17,96,554,113,189,14,97,555,111,187,12,98,556,112,188,13,697,698,700,699,643,38,655,626,33,641,36,627,653,34,628,37,642,654,35,41,639,651,629,32,39,640,652,630,30,40,638,650,631,31,634,44,646,624,24,632,42,644,625,25,633,43,645,623,26,637,47,649,620,27,635,45,647,621,28,636,46,648,622,29,661,662,664,663,331,79,341,310,303,329,80,308,342,304,309,78,330,343,302,82,327,340,313,306,83,328,338,311,307,81,326,339,312,305,322,77,332,316,301,320,75,333,314,299,321,76,334,315,300,325,73,335,319,297,323,74,336,317,298,324,72,337,318,296,682,681,684,683,126,568,235,213,208,124,566,214,233,209,215,567,125,234,207,571,122,231,212,204,569,123,232,210,205,570,121,230,211,206,221,563,226,219,199,120,564,225,220,200,657,565,658,656,659,224,562,229,218,202,222,560,227,216,203,223,561,228,217,201,693,694,696,695,516,177,526,501,545,517,175,502,524,546,500,176,515,525,547,180,512,529,504,544,178,513,527,505,542,179,514,528,503,543,522,183,532,507,536,523,181,530,508,537,521,182,531,506,538,518,186,535,510,539,519,184,533,511,540,520,185,534,509,541,666,665,668,667,381,87,355,377,367,382,88,378,353,365,379,89,380,354,366,86,384,351,376,363,84,385,352,374,364,85,383,350,375,362,387,93,346,368,358,388,94,344,369,356,386,95,345,370,357,390,92,349,371,361,391,90,347,372,359,389,91,348,373,360,674,673,676,675 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#9f23da9903d6ebc1c6f98cbe23264669be86f8e7144737b42fbccbf8aeddcd62, M = {60} 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 19:20:16 · history