Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma a34a077f2041…

magma a34a077f2041
Size
705
Isomorphism class hash
a34a077f204154ac21f43cd2ec368fa1d9af6b138bdc0672939a0637fc6036aa
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 17:43:29
Display reorder
704,503,469,457,482,501,470,458,480,502,468,456,481,499,472,460,485,500,473,461,483,498,471,459,484,463,494,475,488,464,492,476,486,462,493,474,487,497,466,478,491,495,467,479,489,496,465,477,490,504,505,506,507,508,509,510,511,515,513,514,512,700,701,703,702,658,657,659,656,650,648,651,649,654,653,655,652,642,641,643,640,646,645,647,644,638,637,639,636,623,622,621,620,615,614,613,612,619,618,617,616,634,635,633,632,626,627,624,625,630,631,629,628,158,156,157,161,159,160,164,162,166,167,165,163,688,689,691,690,297,273,56,285,298,274,54,286,299,275,55,287,296,272,59,284,294,270,57,282,295,271,58,283,51,288,264,276,52,289,265,277,53,290,266,278,291,50,267,279,292,48,268,280,293,49,269,281,310,311,309,306,307,308,301,302,303,304,305,300,675,674,672,673,378,401,42,368,379,399,43,366,380,400,44,367,381,397,45,371,382,398,46,369,383,396,47,370,40,376,407,363,41,377,405,364,39,375,406,365,372,36,403,362,373,37,404,360,374,38,402,361,395,393,394,391,392,390,386,384,388,389,387,385,682,683,681,680,183,206,66,178,184,204,67,179,185,205,68,177,182,209,69,174,180,207,70,175,181,208,71,176,64,189,212,169,65,190,210,170,63,191,211,168,188,60,215,172,186,61,213,173,187,62,214,171,197,195,196,193,194,192,203,201,198,199,200,202,695,692,693,694,422,455,8,412,420,453,6,413,421,454,7,411,425,451,11,408,423,452,9,409,424,450,10,410,3,428,446,418,4,426,444,419,5,427,445,417,431,2,449,414,429,1,447,415,430,0,448,416,442,443,441,438,439,440,433,434,435,436,437,432,696,697,698,699,529,554,14,517,530,552,12,518,528,553,13,516,532,557,17,520,533,555,15,521,531,556,16,519,20,535,560,523,18,536,558,524,19,534,559,522,538,23,563,526,539,21,561,527,537,22,562,525,542,540,541,545,543,544,548,546,550,551,549,547,686,685,684,687,220,245,97,259,221,243,98,260,219,244,96,258,216,241,100,262,217,242,101,263,218,240,99,261,103,226,251,257,104,227,249,255,102,225,250,256,222,106,247,253,223,107,248,254,224,105,246,252,229,230,228,232,233,231,235,236,237,238,239,234,662,663,661,660,334,350,24,314,335,348,25,312,333,349,26,313,330,353,27,317,331,351,28,315,332,352,29,316,30,325,356,320,31,326,354,318,32,324,355,319,328,33,359,323,329,34,357,321,327,35,358,322,341,339,340,337,338,336,347,345,342,343,344,346,679,678,676,677,130,145,88,117,131,146,89,118,129,144,87,119,126,148,84,116,127,149,85,114,128,147,86,115,94,121,151,108,95,122,152,109,93,120,150,110,124,90,154,111,125,91,155,112,123,92,153,113,137,135,136,133,134,132,143,141,138,139,140,142,666,667,665,664,569,594,72,611,567,595,73,609,568,596,74,610,565,597,75,607,566,598,76,608,564,599,77,606,78,575,592,602,79,573,593,600,80,574,591,601,571,81,588,605,572,82,589,603,570,83,590,604,584,582,583,587,585,586,579,580,577,578,576,581,668,671,670,669 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#616ee92b4c2e3f87630606dae5e5d5a5d531c0e51b30b7b61db0c949f5d47644, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 17:43:30 · history