Equation 677 Database

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Magma a6eddfbd1021…

magma a6eddfbd1021
Size
705
Isomorphism class hash
a6eddfbd1021f33fb3a374eb8e3eb98fd177a788ed0666fa3934fdb5a09215c9
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 21:12:28
Display reorder
660,106,462,463,474,460,107,428,434,421,422,105,442,443,457,441,102,523,522,537,521,103,483,482,497,481,104,503,502,517,501,584,97,583,597,580,557,544,98,543,540,564,96,563,577,560,100,644,643,657,641,101,604,603,617,600,99,624,623,637,621,699,697,691,687,221,464,461,471,466,219,420,427,424,423,220,446,440,454,448,217,520,526,534,528,218,480,486,494,488,216,500,506,514,508,582,227,586,594,588,554,542,225,546,548,562,226,566,574,568,223,642,646,654,648,224,602,606,614,608,222,622,626,634,628,694,693,689,698,11,184,362,314,169,9,360,312,170,185,10,183,361,313,168,7,365,180,317,172,8,363,181,315,173,6,364,182,316,171,368,2,190,320,175,318,366,1,191,176,367,0,189,319,174,5,371,186,323,178,3,369,187,321,179,4,370,188,322,177,666,679,668,673,287,410,374,338,86,285,372,336,84,408,286,409,373,337,85,283,377,413,341,89,284,375,411,339,87,282,376,412,340,88,380,278,416,344,92,342,378,276,414,90,379,277,415,343,91,281,383,419,347,95,279,381,417,345,93,280,382,418,346,94,670,671,683,675,235,468,465,475,470,236,429,435,431,430,234,450,447,459,452,238,527,530,539,532,239,487,490,499,492,237,507,510,519,512,587,233,590,599,592,559,547,231,550,552,567,232,570,579,572,229,647,650,659,652,230,607,610,619,612,228,627,630,639,632,702,700,695,696,64,477,478,476,479,65,439,436,438,437,63,445,458,444,453,60,538,525,524,533,61,498,485,484,493,62,518,505,504,513,598,70,581,585,593,545,558,71,541,553,578,69,561,565,573,66,658,640,645,653,67,618,601,605,613,68,638,620,625,633,703,692,686,701,119,472,469,467,473,117,426,425,433,432,118,455,451,449,456,115,531,535,529,536,116,491,495,489,496,114,511,515,509,516,591,110,595,589,596,549,551,108,555,556,571,109,575,569,576,113,651,655,649,656,111,611,615,609,616,112,631,635,629,636,685,690,704,688,200,269,208,248,263,198,209,246,261,267,199,268,207,247,262,203,204,265,251,259,201,205,266,249,260,202,206,264,250,258,214,195,275,243,254,244,215,196,273,252,213,197,274,245,253,194,210,271,242,257,192,211,272,240,255,193,212,270,241,256,662,681,663,665,28,23,54,350,398,26,55,348,396,21,27,22,56,349,397,24,57,19,353,401,47,58,20,351,399,25,59,18,352,400,52,34,14,356,404,354,53,32,12,402,51,33,13,355,403,30,48,17,359,407,31,49,15,357,405,29,50,16,358,406,672,682,676,684,75,161,290,386,326,76,288,384,324,159,77,160,289,385,325,74,293,157,389,329,72,291,158,387,327,73,292,156,388,328,296,81,167,392,332,390,294,82,165,330,295,83,166,391,331,80,299,163,395,335,78,297,164,393,333,79,298,162,394,334,680,667,678,661,39,142,145,302,127,40,146,300,128,143,38,141,144,301,126,35,148,138,305,130,36,149,139,303,131,37,147,140,304,129,151,45,133,308,125,306,152,46,134,123,150,44,132,307,124,41,154,136,311,121,42,155,137,309,122,43,153,135,310,120,664,677,674,669 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#dd5d8cb242321da00ce62fc2d476849be658b6b0a3d2fd229095425016dc303c, 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 21:12:29 · history