Equation 677 Database

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Magma a3ad2e134ee4…

magma a3ad2e134ee4
Size
705
Isomorphism class hash
a3ad2e134ee46d011c6f68d37a423c6d4fce2b6f0c6335a99ef86d08a284bbfb
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 21:57:11
Display reorder
660,53,397,404,386,412,51,398,402,384,413,52,396,403,385,411,393,49,400,382,415,394,401,383,416,50,395,48,399,381,414,59,410,388,377,418,57,408,389,375,419,58,409,387,376,417,406,55,391,380,421,378,407,56,392,422,405,54,390,379,420,685,686,688,687,493,88,299,74,165,494,89,297,72,166,492,87,298,73,167,84,489,302,77,168,85,300,75,169,490,86,491,301,76,170,484,294,94,80,163,485,295,95,78,164,483,296,93,79,162,293,487,90,83,159,81,291,488,91,160,292,486,92,82,161,701,702,704,703,36,606,623,134,367,37,607,621,132,368,38,608,622,133,366,609,39,619,130,363,610,620,131,364,40,611,41,618,129,365,42,614,604,125,373,43,612,605,123,374,44,613,603,124,372,617,45,600,128,369,126,615,46,601,370,616,47,602,127,371,670,669,672,671,501,309,171,28,67,502,310,172,29,68,503,311,173,27,66,312,504,174,24,70,313,175,25,71,505,314,506,176,26,69,499,177,307,34,65,500,178,308,35,63,498,179,306,33,64,180,495,303,30,61,31,181,496,304,62,182,497,305,32,60,680,677,679,678,317,536,544,519,512,315,534,545,520,510,316,535,543,521,511,532,320,547,522,508,533,548,523,509,318,531,319,546,524,507,323,550,542,525,518,321,551,540,526,516,322,549,541,527,517,553,326,538,528,514,529,554,324,539,515,552,325,537,530,513,689,690,691,692,212,219,235,350,585,210,220,236,348,586,211,221,234,349,587,222,208,231,346,588,223,232,347,589,209,224,207,233,345,590,218,241,225,341,583,216,242,226,339,584,217,240,227,340,582,237,214,228,344,579,342,238,215,229,580,239,213,230,343,581,697,698,700,699,147,630,647,142,6,148,631,645,143,7,149,632,646,141,8,633,150,643,145,9,634,644,146,10,151,635,152,642,144,11,153,638,628,140,4,154,636,629,138,5,155,637,627,139,3,641,156,624,136,1,137,639,157,625,0,640,158,626,135,2,661,662,664,663,245,440,447,423,464,243,438,448,424,462,244,439,449,425,463,436,248,450,426,460,437,451,427,461,246,435,247,452,428,459,251,453,446,429,470,249,454,444,430,468,250,455,445,431,469,456,254,442,432,466,433,457,252,443,467,458,253,441,434,465,682,681,684,683,354,96,595,114,109,355,97,596,115,110,356,98,594,116,108,99,353,598,113,105,100,599,111,106,351,101,352,597,112,107,360,655,652,654,653,361,659,656,658,657,362,650,649,648,651,592,359,120,119,103,117,593,357,121,104,591,358,122,118,102,693,694,696,695,327,569,183,563,200,328,567,184,561,198,329,568,185,562,199,572,330,186,566,196,570,187,564,197,331,571,332,188,565,195,333,189,575,558,206,334,190,573,559,204,335,191,574,560,205,192,336,578,557,202,555,193,337,576,203,194,338,577,556,201,666,665,668,667,480,282,15,269,262,481,283,16,267,263,482,284,17,268,261,281,479,14,272,265,279,12,270,266,477,280,478,13,271,264,471,21,288,275,260,472,22,289,273,258,473,23,290,274,259,20,474,287,278,256,276,18,475,285,257,19,476,286,277,255,674,673,676,675 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#fdf5f382e471d95c048f9fa2e9b8340aa5eb614276b1c155a6fb7129b8435eb8, 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 21:57:12 · history