Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma ec22b4a7cd26…

magma ec22b4a7cd26
Size
705
Isomorphism class hash
ec22b4a7cd26058d250236fda4cc1fe47e53de547933530d3a33c2cab74bcf68
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 18:17:40
Display reorder
660,530,107,533,538,521,490,105,493,498,480,510,106,513,518,500,103,453,454,455,448,104,469,471,475,460,102,429,431,435,421,650,98,653,658,640,610,96,613,618,601,630,97,633,638,620,101,570,573,578,561,99,590,593,598,581,100,550,553,558,540,687,691,701,699,534,5,529,532,524,494,3,489,492,484,514,4,509,512,504,0,445,443,444,442,2,472,468,470,463,1,432,428,430,423,654,11,649,652,644,614,9,609,612,604,634,10,629,632,624,7,574,569,572,564,8,594,589,592,584,6,554,549,552,544,692,685,703,690,151,24,233,161,74,152,25,231,159,72,150,26,232,160,73,27,154,229,157,77,28,155,230,158,75,29,153,228,156,76,149,30,239,167,80,147,31,237,165,78,148,32,238,166,79,33,145,235,163,83,34,146,236,164,81,35,144,234,162,82,670,661,665,682,377,65,353,389,341,375,63,351,387,339,376,64,352,388,340,61,373,349,385,337,62,374,350,386,338,60,372,348,384,336,383,71,359,395,347,381,69,357,393,345,382,70,358,394,346,67,379,355,391,343,68,380,356,392,344,66,378,354,390,342,677,673,672,680,527,16,525,528,526,487,17,485,488,486,507,15,505,508,506,12,451,449,452,450,13,466,464,467,465,14,426,424,427,425,647,22,645,648,646,607,23,605,608,606,627,21,625,628,626,18,567,565,568,566,19,587,585,588,586,20,547,545,548,546,700,694,696,698,535,36,520,531,539,495,37,481,491,499,515,38,501,511,519,39,458,457,456,459,40,478,477,476,479,41,438,437,436,439,655,42,642,651,659,615,43,602,611,619,635,44,622,631,639,45,575,562,571,579,46,595,582,591,599,47,555,542,551,559,693,697,686,688,522,112,536,537,523,482,113,496,497,483,502,111,516,517,503,108,440,446,447,441,109,462,473,474,461,110,422,433,434,420,643,118,656,657,641,603,119,616,617,600,623,117,636,637,621,114,563,576,577,560,115,583,596,597,580,116,543,556,557,541,704,695,702,689,329,52,222,401,191,327,53,223,399,189,328,51,224,400,190,48,325,225,397,187,49,326,226,398,188,50,324,227,396,186,335,58,220,407,182,333,59,221,405,180,334,57,219,406,181,54,331,216,403,185,55,332,217,404,183,56,330,218,402,184,671,679,678,683,269,135,85,413,259,267,136,86,411,260,268,137,84,412,258,134,265,88,409,262,132,266,89,410,263,133,264,87,408,261,275,141,91,419,257,273,142,92,417,255,274,143,90,418,256,140,271,94,415,253,138,272,95,416,254,139,270,93,414,252,663,681,676,684,281,169,293,365,305,279,170,291,363,303,280,168,292,364,304,172,277,289,361,301,173,278,290,362,302,171,276,288,360,300,287,175,299,371,311,285,176,297,369,309,286,174,298,370,310,178,283,295,367,307,179,284,296,368,308,177,282,294,366,306,664,667,668,675,199,123,244,207,317,200,124,245,208,315,198,125,243,209,316,122,202,240,206,313,120,203,241,204,314,121,201,242,205,312,197,129,250,213,323,195,130,251,214,321,196,131,249,215,322,128,193,246,212,319,126,194,247,210,320,127,192,248,211,318,674,662,669,666 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#7662547f1ab019fdebb7f412cf128566d4c1d6f1fe751ad78d224fe85422d2cf, 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 18:17:41 · history