Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 607cba78b6c7…

magma 607cba78b6c7
Size
705
Isomorphism class hash
607cba78b6c7d59f09669822f7e31cc2cac988bd16e94d538c5dbfa117702cff
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 16:24:34
Display reorder
704,76,38,30,69,77,36,31,70,37,75,32,71,72,41,33,68,73,39,34,66,74,40,35,67,82,44,28,60,83,42,29,61,81,43,27,62,78,47,24,63,79,45,25,64,80,46,26,65,58,59,57,54,55,56,49,50,51,52,53,48,683,680,682,681,545,118,98,86,543,119,96,84,117,544,97,85,541,114,101,89,542,115,99,87,540,116,100,88,551,109,104,92,549,110,102,90,550,108,103,91,547,112,107,95,548,113,105,93,546,111,106,94,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,9,402,432,422,10,403,433,420,404,11,434,421,8,405,435,425,6,406,436,423,7,407,437,424,1,400,438,428,0,401,439,426,2,399,440,427,3,396,441,431,4,397,442,429,5,398,443,430,410,408,409,413,411,412,416,414,418,419,417,415,669,671,668,670,182,367,352,341,180,368,353,339,366,181,351,340,185,370,348,337,183,371,349,338,184,369,350,336,188,365,358,347,186,363,359,345,187,364,357,346,191,361,354,343,189,362,355,344,190,360,356,342,372,373,374,375,376,377,378,379,383,381,382,380,679,676,678,677,252,524,509,496,253,522,507,497,523,254,508,495,255,527,505,492,256,525,506,493,257,526,504,494,258,519,515,502,259,520,513,503,260,521,514,501,261,518,511,498,262,516,512,499,263,517,510,500,530,528,529,533,531,532,536,534,538,539,537,535,689,690,688,691,275,608,638,626,273,606,636,624,607,274,637,625,271,611,641,629,272,609,639,627,270,610,640,628,266,603,644,632,264,604,642,630,265,605,643,631,269,602,647,635,267,600,645,633,268,601,646,634,614,612,613,617,615,616,620,618,622,623,621,619,692,694,693,695,18,467,446,483,19,465,444,484,466,20,445,485,21,463,449,482,22,464,447,480,23,462,448,481,16,458,452,489,17,456,450,490,15,457,451,491,12,461,455,488,13,459,453,486,14,460,454,487,473,471,472,469,470,468,479,477,474,475,476,478,661,662,660,663,240,302,294,284,241,300,295,282,301,242,296,283,243,305,297,287,244,303,298,285,245,304,299,286,246,308,292,279,247,306,293,280,248,307,291,281,249,311,288,278,250,309,289,276,251,310,290,277,321,322,323,320,318,319,312,313,317,315,316,314,685,686,684,687,331,141,171,161,332,142,172,159,143,330,173,160,334,140,170,157,335,138,168,158,333,139,169,156,329,132,177,167,327,133,178,165,328,134,179,166,325,135,176,163,326,136,174,164,324,137,175,162,147,148,149,146,144,145,153,154,151,152,150,155,698,697,699,696,395,233,227,213,393,231,225,214,232,394,226,215,391,229,223,212,392,230,224,210,390,228,222,211,386,239,218,204,384,237,216,205,385,238,217,206,389,235,221,207,387,236,219,208,388,234,220,209,201,202,203,200,198,199,192,193,197,195,196,194,666,665,667,664,123,555,594,584,124,556,595,582,557,125,596,583,122,554,597,587,120,552,598,585,121,553,599,586,129,561,592,579,130,562,593,580,131,563,591,581,128,560,588,578,126,558,589,576,127,559,590,577,571,572,570,574,575,573,569,567,564,565,566,568,674,673,675,672 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#3180ad8dfd10ba7152583c35a71774bceecf2852df6e850dd8c0dada693f6036, 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 16:24:35 · history