Equation 677 Database

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Magma eeefb846756d…

magma eeefb846756d
Size
705
Isomorphism class hash
eeefb846756dcf36846aaa3896a0d510dd06163245e93babea446fbbcbf5e38d
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 20:06:41
Display reorder
660,206,533,528,526,522,204,482,493,488,486,205,502,513,508,506,454,209,447,451,450,473,207,461,468,466,433,208,422,428,426,212,642,653,648,646,602,613,608,210,606,633,622,628,211,626,562,573,568,215,566,582,593,588,213,586,542,553,548,214,546,700,685,697,695,101,538,524,530,521,99,481,498,484,490,100,501,518,504,510,455,97,440,441,444,475,98,460,464,470,435,96,421,424,430,107,641,658,644,650,601,618,604,105,610,638,621,624,106,630,561,578,564,103,570,580,598,584,104,590,541,558,544,102,550,686,689,692,696,10,329,377,305,257,11,255,327,375,303,9,256,328,376,304,325,6,253,373,301,326,7,254,374,302,324,8,252,372,300,0,263,335,383,311,261,333,381,2,309,334,262,382,1,310,259,331,379,4,307,260,332,380,5,308,258,330,378,3,306,674,666,668,663,200,75,12,389,401,198,399,76,13,387,199,400,77,14,388,74,203,397,15,385,72,201,398,16,386,73,202,396,17,384,195,407,81,18,395,405,82,19,196,393,83,406,20,197,394,403,80,21,194,391,404,78,22,192,392,402,79,23,193,390,682,676,662,677,121,535,520,532,523,122,483,495,480,492,120,503,515,500,512,457,124,449,448,453,478,125,463,462,472,437,123,423,420,432,127,643,655,640,652,603,615,600,128,612,635,623,620,126,632,563,575,560,130,572,583,595,581,131,592,543,555,540,129,552,703,694,699,702,49,529,536,539,537,50,497,489,496,499,48,517,509,516,519,452,52,456,458,459,469,53,477,476,479,429,51,436,438,439,55,657,649,656,659,617,609,616,56,619,629,637,636,54,639,577,569,576,58,579,597,589,596,59,599,557,549,556,57,559,691,690,688,701,222,527,525,534,531,223,491,487,485,494,224,511,507,505,514,443,225,445,442,446,467,226,471,465,474,427,227,431,425,434,220,651,647,645,654,611,607,605,221,614,627,631,625,219,634,571,567,565,216,574,591,587,585,217,594,551,547,545,218,554,704,698,687,693,25,66,88,365,317,26,315,67,89,363,24,316,68,87,364,69,28,313,84,361,70,29,314,85,362,71,27,312,86,360,31,323,64,94,371,321,65,95,32,369,63,322,93,30,370,319,60,90,34,367,320,61,91,35,368,318,62,92,33,366,678,672,680,667,187,161,46,341,413,188,411,159,47,339,186,412,160,45,340,157,190,409,42,337,158,191,410,43,338,156,189,408,44,336,185,419,167,37,347,417,165,38,183,345,166,418,36,184,346,415,163,40,181,343,416,164,41,182,344,414,162,39,180,342,673,669,681,684,291,140,269,111,353,292,351,138,267,112,293,352,139,268,113,143,290,349,265,110,141,288,350,266,108,142,289,348,264,109,297,359,135,275,117,357,136,273,298,118,137,358,274,299,119,355,134,271,296,116,356,132,272,294,114,354,133,270,295,115,664,671,675,670,174,281,234,145,245,175,243,279,235,146,176,244,280,236,144,277,177,241,237,148,278,178,242,238,149,276,179,240,239,147,172,251,287,232,151,249,285,233,173,152,286,250,231,171,150,247,283,228,168,154,248,284,229,169,155,246,282,230,170,153,679,683,665,661 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#b9c83ee29c9828886a1d9280722af908f3a23a39dfe3e8d4571f7572270a5310, 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 20:06:42 · history