Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 4772d8ef3955…

magma 4772d8ef3955
Size
705
Isomorphism class hash
4772d8ef3955000ad8a508d1d6b666e7fcc4fb9464d5fb527d49f67eaec65302
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 18:18:30
Display reorder
660,466,99,465,461,470,100,431,429,424,421,101,453,447,446,441,528,533,98,527,521,488,493,96,487,480,508,513,97,507,501,593,105,587,588,581,553,106,547,548,541,573,107,567,568,561,653,104,647,648,640,608,613,102,607,600,633,103,627,628,620,693,689,697,695,460,49,471,467,468,50,426,420,427,425,48,449,440,454,448,522,530,52,534,529,482,490,53,494,489,502,510,51,514,509,590,55,594,582,589,550,56,554,542,549,570,54,574,562,569,650,58,654,642,649,602,610,59,614,609,630,57,634,622,629,690,686,692,694,230,111,226,242,259,112,260,228,227,240,113,258,229,225,241,233,262,110,222,245,231,263,108,223,243,232,261,109,224,244,257,117,217,236,248,255,118,218,234,246,256,119,216,235,247,253,116,220,239,251,237,254,114,221,249,252,115,219,238,250,673,661,663,677,193,74,278,410,274,72,275,194,276,408,73,273,192,277,409,196,270,77,281,413,197,271,75,279,411,195,272,76,280,412,265,80,284,199,416,266,78,282,200,414,264,79,283,198,415,268,83,287,202,419,203,269,81,285,417,267,82,286,201,418,681,662,683,664,469,122,473,472,474,120,434,430,433,432,121,458,450,456,455,531,538,125,536,535,491,498,123,496,495,511,518,124,516,515,598,128,596,591,595,558,126,556,551,555,578,127,576,571,575,658,131,656,651,655,611,618,129,616,615,638,130,636,631,635,700,691,702,698,476,85,477,478,479,86,436,437,438,439,84,451,452,444,457,520,532,88,525,537,481,492,89,485,497,500,512,87,505,517,592,91,585,580,597,552,92,545,540,557,572,90,565,560,577,652,94,645,641,657,601,612,95,605,617,632,93,625,621,637,703,701,699,688,464,4,475,462,463,5,422,423,435,428,3,443,445,459,442,526,524,1,539,523,486,484,0,499,483,506,504,2,519,503,584,10,599,586,583,544,11,559,546,543,564,9,579,566,563,644,6,659,646,643,606,604,7,619,603,624,8,639,626,623,685,687,704,696,314,66,20,141,374,67,372,312,18,142,68,373,313,19,143,317,377,69,23,140,315,375,70,21,138,316,376,71,22,139,380,64,15,320,132,378,65,16,318,133,379,63,17,319,134,383,60,14,323,135,321,381,61,12,136,382,62,13,322,137,678,669,675,672,398,214,181,160,178,215,179,396,182,161,213,177,397,180,159,401,174,210,184,156,399,175,211,185,157,400,176,212,183,158,169,205,187,404,166,170,206,188,402,167,168,204,186,403,165,172,208,190,407,162,405,173,209,191,163,171,207,189,406,164,680,682,665,684,350,36,326,386,362,37,360,348,324,384,38,361,349,325,385,353,365,39,329,389,351,363,40,327,387,352,364,41,328,388,368,42,332,356,392,366,43,330,354,390,367,44,331,355,391,371,45,335,359,395,357,369,46,333,393,370,47,334,358,394,676,674,679,670,24,151,302,338,290,152,288,25,300,336,150,289,26,301,337,27,293,154,305,341,28,291,155,303,339,29,292,153,304,340,296,149,308,30,344,294,147,306,31,342,295,148,307,32,343,299,145,311,33,347,34,297,146,309,345,298,144,310,35,346,666,668,671,667 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#789271f8e1620c5f8875a1b32dfd6da1b71c443ca3fc9082ace33bb0fcd8a22c, 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 18:18:31 · history