Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma b43e7e381370…

magma b43e7e381370
Size
705
Isomorphism class hash
b43e7e381370553a6a6e1cad7ca6a2aeed1e80a136e3f88912a6aa3037cc3cbb
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 19:12:48
Display reorder
660,0,296,291,114,311,112,2,297,292,312,298,113,3,290,313,117,4,299,294,310,115,5,300,295,308,116,6,301,293,309,7,302,289,109,317,8,303,287,110,318,9,304,288,111,319,10,305,285,108,316,11,306,286,106,314,12,307,284,107,315,685,686,688,687,380,407,396,36,375,37,381,408,397,376,409,35,382,395,374,39,383,406,392,378,40,384,404,393,379,38,385,405,394,377,386,413,402,42,373,387,414,403,43,371,388,415,401,41,372,389,412,398,45,369,390,410,399,46,370,391,411,400,44,368,701,702,704,703,245,271,257,590,272,591,246,269,258,273,270,592,247,259,274,593,244,267,256,275,594,242,268,254,276,595,243,266,255,277,236,262,248,588,278,237,260,249,589,279,238,261,250,587,280,239,265,251,584,281,240,263,252,585,282,241,264,253,586,283,670,669,672,671,451,416,453,155,433,153,449,417,454,431,418,154,450,452,432,158,447,419,456,429,156,448,420,457,430,157,446,421,455,428,442,422,459,161,439,440,423,460,159,437,441,424,458,160,438,445,425,462,164,435,443,426,463,162,436,444,427,461,163,434,680,677,679,678,58,179,172,472,99,470,59,177,173,97,178,471,57,171,98,475,54,182,175,95,473,55,180,176,96,474,56,181,174,94,1,185,170,467,105,75,183,168,468,103,78,184,169,469,104,83,188,166,466,101,87,186,167,464,102,90,187,165,465,100,689,690,691,692,524,553,540,202,571,203,525,551,541,569,552,201,526,539,570,205,527,549,536,567,206,528,550,537,568,204,529,548,538,566,530,559,546,208,562,531,557,547,209,560,532,558,545,207,561,533,555,542,211,565,534,556,543,212,563,535,554,544,210,564,697,698,700,699,641,612,655,600,625,601,642,613,653,623,611,599,643,654,624,596,640,608,651,621,597,638,609,652,622,598,639,610,650,620,632,618,646,606,631,633,619,644,607,629,634,617,645,605,630,635,614,649,602,627,636,615,647,603,628,637,616,648,604,626,661,662,664,663,125,334,327,131,60,132,126,332,328,61,333,130,124,326,62,134,128,337,330,63,135,129,335,331,64,133,127,336,329,65,123,340,325,137,88,121,338,323,138,92,122,339,324,136,84,119,343,321,140,66,120,341,322,141,76,118,342,320,139,80,682,681,684,683,18,216,233,574,148,572,19,217,234,149,218,573,17,235,147,577,14,215,232,151,575,15,213,230,152,576,16,214,231,150,224,222,225,580,146,13,223,226,578,142,657,656,658,579,659,20,221,227,583,145,21,219,228,581,143,22,220,229,582,144,693,694,696,695,511,481,512,189,497,190,509,479,513,498,480,191,510,514,499,192,507,477,515,496,193,508,478,516,494,194,506,476,517,495,502,487,518,195,488,500,485,519,196,489,501,486,520,197,490,505,483,521,198,491,503,484,522,199,492,504,482,523,200,493,666,665,668,667,367,25,82,71,352,72,365,23,86,350,24,70,366,91,351,67,363,28,79,355,68,364,26,53,353,69,362,27,74,354,358,31,47,73,347,356,29,48,77,348,357,30,49,81,349,361,34,50,85,346,359,32,51,89,344,360,33,52,93,345,674,673,676,675 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#90fd68087a2f09648803d65723dcc8788b62f036d4e0ed1478893fb37d6a20cd, 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 19:12:49 · history