Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 0ddcb57fa70b…

magma 0ddcb57fa70b
Size
705
Isomorphism class hash
0ddcb57fa70b26452074c9a56f2a33c554e4a367eb24b3d04fabfaacb9e5d61c
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 21:16:35
Display reorder
660,561,568,0,571,576,581,588,596,2,591,540,548,556,1,551,620,628,636,4,631,641,648,656,5,651,600,608,616,3,611,536,521,7,528,531,496,480,8,488,491,516,500,6,508,511,440,449,10,443,445,460,476,11,468,471,421,436,9,428,431,695,703,689,697,577,572,206,574,573,597,592,593,204,594,557,552,553,205,554,637,632,633,209,634,657,652,653,207,654,617,612,613,208,614,533,537,212,532,534,493,497,210,492,494,513,517,211,512,514,457,456,215,446,447,477,473,213,472,474,437,433,214,432,434,690,700,698,702,84,114,242,28,234,85,115,235,240,29,86,116,236,241,27,87,117,237,245,24,88,118,238,243,25,89,119,239,244,26,232,90,248,112,34,233,91,246,113,35,231,92,247,111,33,93,228,251,108,30,94,229,249,109,31,95,230,250,110,32,673,671,675,665,178,151,17,331,355,179,152,356,15,332,177,150,354,16,330,174,154,358,13,334,175,155,359,14,335,176,153,357,12,333,353,169,23,149,329,351,170,21,147,327,352,168,22,148,328,172,349,19,145,325,173,350,20,146,326,171,348,18,144,324,676,664,667,670,575,565,72,566,570,595,585,590,73,586,555,545,550,74,546,635,625,630,75,626,655,645,650,76,646,615,605,610,77,606,530,535,78,525,526,490,495,79,485,486,510,515,80,505,506,448,444,81,452,453,475,470,82,465,466,435,430,83,425,426,685,694,704,687,563,567,133,569,562,583,587,582,134,589,543,547,542,132,549,623,627,622,136,629,643,647,642,137,649,603,607,602,135,609,522,523,139,527,529,482,483,140,487,489,502,503,138,507,509,451,450,142,454,455,463,462,143,467,469,423,422,141,427,429,688,693,701,686,578,560,164,564,579,599,580,598,162,584,558,541,559,163,544,638,621,639,167,624,659,640,658,165,644,619,601,618,166,604,539,538,159,520,524,498,499,160,481,484,519,518,161,501,504,458,459,158,441,442,479,478,156,461,464,438,439,157,420,424,699,692,696,691,319,411,195,410,104,320,412,102,196,413,318,409,103,197,408,322,417,107,194,416,323,418,105,192,419,321,415,106,193,414,99,317,201,406,407,100,315,202,402,403,101,316,203,404,405,313,98,200,398,399,314,96,198,401,400,312,97,199,396,397,681,666,682,668,367,307,53,387,386,368,308,389,51,388,366,306,384,52,385,370,310,392,49,393,371,311,395,50,394,369,309,390,48,391,383,365,59,305,382,379,363,57,303,378,381,364,58,304,380,361,374,55,301,375,362,376,56,302,377,360,373,54,300,372,663,672,678,677,343,259,223,127,274,344,260,275,224,128,342,258,273,222,126,346,262,270,226,130,347,263,271,227,131,345,261,272,225,129,265,341,221,257,125,266,339,219,255,123,264,340,220,256,124,337,268,217,253,121,338,269,218,254,122,336,267,216,252,120,661,669,680,679,298,67,190,44,282,299,68,283,191,42,297,66,284,189,43,294,70,285,186,47,295,71,286,187,45,296,69,287,188,46,280,289,181,65,39,281,290,182,63,40,279,288,180,64,41,292,276,184,61,38,293,277,185,62,36,291,278,183,60,37,674,683,662,684 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#e2a478bba1a9cde7c476f091d01301457f542f6a1b857d9784efc8df77c998e9, 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 21:16:35 · history