Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma e1eb5651fca4…

magma e1eb5651fca4
Size
705
Isomorphism class hash
e1eb5651fca4c0ff4fcff0074a64acf266990da721a16f76d71736fb53da90e7
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 15:11:38
Display reorder
660,162,397,377,175,392,375,163,176,398,390,376,396,164,174,391,380,161,171,393,388,378,159,172,394,389,379,160,173,395,387,372,153,166,403,383,373,154,167,404,381,374,155,165,402,382,371,156,169,399,386,369,157,170,400,384,370,158,168,401,385,685,686,688,687,467,455,479,224,443,477,465,222,453,441,478,454,466,223,442,482,470,220,458,446,480,468,221,456,444,481,469,219,457,445,485,473,215,461,449,483,471,213,459,447,484,472,214,460,448,488,476,218,464,452,486,474,216,462,450,487,475,217,463,451,701,702,704,703,321,359,338,619,347,336,322,617,357,345,337,358,323,618,346,334,324,615,362,350,335,325,616,360,348,333,326,614,361,349,344,327,610,365,353,342,328,608,363,351,343,329,609,364,352,340,330,613,368,356,341,331,611,366,354,339,332,612,367,355,670,669,672,671,512,497,518,230,527,516,510,228,495,525,517,496,511,229,526,514,508,226,500,530,515,509,227,498,528,513,507,225,499,529,524,503,236,492,533,522,501,234,493,531,523,502,235,494,532,520,506,232,491,536,521,504,233,489,534,519,505,231,490,535,680,677,679,678,545,246,558,50,571,559,543,51,247,572,560,248,544,52,570,557,548,53,245,567,555,546,54,243,568,556,547,55,244,569,549,540,48,237,562,550,541,49,238,563,551,542,47,239,561,552,539,44,240,565,553,537,45,241,566,554,538,46,242,564,689,690,691,692,64,298,77,105,593,78,62,106,299,591,79,297,63,104,592,76,67,108,301,596,74,65,109,302,594,75,66,107,300,595,68,59,111,304,588,69,60,112,305,589,70,61,110,303,590,71,58,114,307,587,72,56,115,308,585,73,57,113,306,586,697,698,700,699,641,628,655,38,5,653,642,39,626,3,654,627,643,40,4,651,640,41,631,0,652,638,42,629,2,650,639,43,630,1,646,632,36,623,11,644,633,37,624,9,645,634,35,625,10,649,635,32,622,7,647,636,33,620,8,648,637,34,621,6,661,662,664,663,428,412,181,85,21,182,426,83,413,22,180,411,427,84,20,177,424,81,415,24,178,425,82,416,25,179,423,80,414,23,187,419,91,410,27,188,417,89,408,28,186,418,90,409,26,183,422,87,406,30,184,420,88,407,31,185,421,86,405,29,682,681,684,683,119,602,16,314,133,14,120,312,603,134,15,604,121,313,135,19,118,310,605,132,17,116,311,606,130,18,117,309,607,131,13,125,320,600,139,12,126,318,601,140,657,656,319,658,659,127,124,316,597,138,128,122,317,598,136,129,123,315,599,137,693,694,696,695,285,278,251,575,261,249,286,573,276,262,250,277,287,574,263,254,288,578,274,264,252,289,576,275,265,253,290,577,273,266,257,291,581,284,267,255,292,579,282,268,256,293,580,283,269,260,294,584,280,270,258,295,582,281,271,259,296,583,279,272,666,665,668,667,198,435,212,102,148,210,199,103,436,149,211,437,200,101,147,208,197,98,438,151,209,195,99,439,152,207,196,100,440,150,203,189,93,433,146,201,190,94,434,144,202,191,92,432,145,206,192,96,429,142,204,193,97,430,143,205,194,95,431,141,674,673,676,675 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#0898d182914656a7d8331eed416fb390a2b0882bf44ec0102530c706a89c62d3, 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 15:11:39 · history