Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma fc33fe44ac10…

magma fc33fe44ac10
Size
705
Isomorphism class hash
fc33fe44ac101a2f411556351587d31bcea969a390f988203952f112f41e115a
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 19:10:01
Display reorder
660,281,267,430,29,172,282,173,265,431,27,266,174,280,432,28,171,277,270,429,25,169,278,268,427,26,170,279,269,428,24,436,262,272,163,35,263,273,164,437,33,264,271,165,438,34,275,261,166,435,31,276,259,167,433,32,274,260,168,434,30,665,672,662,661,41,225,370,490,109,39,110,223,371,491,224,111,40,372,492,112,37,228,369,489,113,38,226,367,487,114,36,227,368,488,376,231,47,107,496,229,45,108,377,497,230,46,106,378,498,43,234,103,375,495,44,232,104,373,493,42,233,105,374,494,686,689,688,685,454,132,122,406,195,455,193,130,123,407,131,194,456,121,408,198,453,128,125,405,196,451,129,126,403,197,452,127,124,404,120,138,460,190,412,136,461,191,118,413,137,462,192,119,414,459,134,189,116,411,457,135,187,117,409,458,133,188,115,410,667,663,666,669,514,442,102,394,241,515,242,443,100,395,444,243,516,101,396,244,513,441,98,393,245,511,439,99,391,246,512,440,97,392,93,448,520,239,400,449,521,240,91,401,450,522,238,92,402,519,447,235,96,399,517,445,236,94,397,518,446,237,95,398,673,675,678,676,585,631,526,418,250,586,251,632,527,419,633,252,587,528,420,249,584,630,525,417,247,582,628,523,415,248,583,629,524,416,532,637,591,256,424,638,592,257,533,425,639,593,258,534,426,590,636,255,531,423,588,634,253,529,421,589,635,254,530,422,668,664,670,671,295,283,502,308,177,296,175,284,503,309,285,176,297,504,307,180,298,286,501,311,178,299,287,499,312,179,300,288,500,310,508,289,301,183,314,290,302,181,509,315,291,303,182,510,313,304,292,186,507,317,305,293,184,505,318,306,294,185,506,316,697,693,695,694,51,571,621,60,69,52,67,572,622,61,573,68,53,623,62,72,54,574,620,59,70,55,575,618,57,71,56,576,619,58,627,577,581,75,66,655,652,73,654,653,656,657,74,659,658,48,578,78,626,65,49,579,76,624,63,50,580,77,625,64,704,703,701,702,478,609,352,550,329,479,330,610,353,551,611,328,480,354,552,325,477,608,351,549,326,475,606,349,547,327,476,607,350,548,343,615,484,320,556,616,485,321,344,557,617,486,319,345,558,483,614,323,346,555,481,612,324,347,553,482,613,322,348,554,700,698,696,699,538,151,466,81,2,539,1,152,467,79,153,0,540,468,80,5,537,154,465,84,3,535,155,463,82,4,536,156,464,83,472,157,544,8,87,158,545,6,473,85,159,546,7,474,86,543,160,11,471,90,541,161,9,469,88,542,162,10,470,89,677,681,679,684,14,211,334,643,364,12,365,212,335,644,213,366,13,336,645,363,17,214,333,642,361,15,215,331,640,362,16,216,332,641,340,217,20,355,649,218,18,356,341,650,219,19,357,342,651,23,220,358,339,648,21,221,359,337,646,22,222,360,338,647,674,683,682,680,143,562,597,382,209,144,210,563,598,383,564,208,142,599,384,205,139,561,596,381,206,140,559,594,379,207,141,560,595,380,603,568,149,200,388,569,150,201,604,389,570,148,199,605,390,145,567,203,602,387,146,565,204,600,385,147,566,202,601,386,691,687,692,690 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#8cce333a947232ca69e33881346ef6b490f8a5c022184a0ee2c46fc59b5e71a5, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 19:10:02 · history