Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 6087e70d5149…

magma 6087e70d5149
Size
705
Isomorphism class hash
6087e70d5149e80667dcca59ea79953046baacb466d7f624004173dd5c25a896
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 21:45:48
Display reorder
660,366,378,390,197,403,195,379,367,391,404,380,196,368,392,402,369,193,381,393,406,370,194,382,394,407,371,192,383,395,405,384,372,203,396,409,385,373,201,397,410,386,374,202,398,408,387,375,199,399,412,376,388,200,400,413,377,389,198,401,411,685,686,688,687,462,476,445,245,450,243,474,463,446,451,475,244,464,444,452,465,241,479,448,453,466,242,477,449,454,467,240,478,447,455,482,468,251,443,456,480,469,249,441,457,481,470,250,442,458,485,471,247,439,459,472,483,248,440,460,473,484,246,438,461,701,702,704,703,334,351,357,611,323,609,352,335,358,321,353,610,333,359,322,330,607,350,356,319,331,608,348,354,320,332,606,349,355,318,342,340,602,363,329,343,341,600,364,327,344,339,601,365,328,345,336,605,362,325,337,346,603,360,326,338,347,604,361,324,670,669,672,671,515,261,494,152,507,150,262,513,492,508,263,151,514,493,509,511,155,260,497,506,512,153,258,495,504,510,154,259,496,505,252,521,147,489,498,253,519,148,490,499,254,520,149,491,500,255,517,146,488,501,518,256,144,486,502,516,257,145,487,503,680,677,679,678,560,522,536,35,546,33,523,558,534,547,524,34,559,535,548,563,31,525,539,549,561,32,526,537,550,562,30,527,538,551,528,566,26,542,552,529,564,24,540,553,530,565,25,541,554,531,569,29,545,555,567,532,27,543,556,568,533,28,544,557,689,690,691,692,289,177,184,104,590,102,178,290,185,588,179,103,288,183,589,292,107,176,180,593,293,105,174,181,591,291,106,175,182,592,168,295,99,190,585,169,296,100,191,586,170,294,101,189,587,171,298,98,186,584,299,172,96,187,582,297,173,97,188,583,697,698,700,699,55,620,635,72,62,73,618,56,633,60,619,74,54,634,61,58,75,623,631,65,59,76,621,632,63,57,77,622,630,64,615,53,78,626,68,616,51,79,624,66,617,52,80,625,67,614,49,81,629,71,50,612,82,627,69,48,613,83,628,70,661,662,664,663,227,123,113,416,212,414,124,225,111,210,125,415,226,112,211,223,419,122,109,215,224,417,120,110,213,222,418,121,108,214,129,218,422,119,207,130,216,420,117,208,131,217,421,118,209,128,221,425,115,206,219,126,423,116,204,220,127,424,114,205,682,681,684,683,315,300,594,134,309,132,301,316,595,310,302,133,317,596,311,314,137,303,597,308,312,135,304,598,306,313,136,305,599,307,640,642,140,643,641,645,646,138,647,644,637,636,139,638,639,653,654,143,655,652,658,657,141,659,656,650,648,142,651,649,693,694,696,695,87,271,277,572,163,570,272,88,278,164,270,571,89,276,162,86,575,274,280,166,84,573,275,281,167,85,574,273,279,165,269,93,578,283,161,267,94,576,284,159,268,95,577,282,160,265,92,581,286,157,90,266,579,287,158,91,264,580,285,156,666,665,668,667,432,44,236,13,2,14,42,433,234,1,43,12,434,235,0,435,16,47,239,5,436,17,45,237,3,437,15,46,238,4,39,430,19,231,8,40,431,20,232,6,41,429,18,233,7,38,426,22,230,11,427,36,23,228,9,428,37,21,229,10,674,673,676,675 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#f3708acaf97ab90d0e627f94c9229dfefc0b06412aed9a05696d0ed9b4a78cdc, 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 21:45:49 · history