Equation 677 Database

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Magma b34a94b29b33…

magma b34a94b29b33
Size
705
Isomorphism class hash
b34a94b29b332964db09562cf3dbfc37f2e5ac3bf3c9b5512e3ca5570e3dada9
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 21:13:05
Display reorder
704,84,139,117,124,125,140,85,118,123,138,86,119,87,120,142,116,88,121,143,114,122,89,141,115,137,130,108,90,135,131,109,91,136,129,110,92,126,133,111,93,127,134,112,94,128,132,113,95,96,97,98,99,100,101,102,103,107,105,106,104,683,680,682,681,38,57,543,63,64,58,36,544,65,59,37,545,41,62,56,542,39,60,54,540,61,40,55,541,48,69,549,44,49,70,550,42,50,71,551,43,68,51,548,47,66,52,546,45,67,53,547,46,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,1,489,504,470,468,490,0,505,469,491,2,506,3,473,488,507,4,471,486,508,472,5,487,509,480,476,510,6,481,474,511,7,482,475,512,8,479,483,513,9,477,484,514,10,478,485,515,11,496,497,495,492,493,494,502,503,500,498,499,501,669,671,668,670,411,271,248,260,258,272,412,246,259,270,413,247,410,263,274,251,408,261,275,249,262,409,273,250,269,255,243,417,267,256,244,418,268,257,245,419,254,265,242,416,252,266,240,414,253,264,241,415,281,279,280,277,278,276,287,285,282,283,284,286,679,676,678,677,538,213,228,194,192,214,539,229,193,215,537,230,534,197,212,231,535,195,210,232,196,536,211,233,204,200,234,529,205,198,235,530,206,199,236,528,203,207,237,532,201,208,238,533,202,209,239,531,220,221,219,216,217,218,226,227,224,222,223,225,689,690,688,691,16,622,638,602,600,623,17,636,601,621,15,637,12,605,618,641,13,603,619,639,604,14,620,640,613,608,644,22,614,606,642,23,612,607,643,21,611,616,647,18,609,617,645,19,610,615,646,20,628,629,627,624,625,626,634,635,632,630,631,633,692,694,693,695,516,184,157,177,178,185,517,158,179,183,518,156,519,176,180,160,520,174,181,161,175,521,182,159,190,168,163,522,191,169,164,523,189,170,162,524,171,186,166,525,172,187,167,526,173,188,165,527,145,146,144,148,149,147,151,152,153,154,155,150,661,662,660,663,310,325,352,315,316,326,311,353,317,324,309,351,306,314,328,348,307,312,329,349,313,308,327,350,331,321,358,301,332,322,359,302,330,323,357,300,320,334,354,304,318,335,355,305,319,333,356,303,347,345,346,343,344,342,338,336,340,341,339,337,685,686,684,687,76,401,383,391,392,399,77,381,390,400,75,382,72,394,397,379,73,395,398,380,393,74,396,378,407,389,374,82,405,387,372,83,406,388,373,81,385,403,377,78,386,404,375,79,384,402,376,80,367,368,366,370,371,369,365,363,360,361,362,364,698,697,699,696,289,453,431,438,439,454,290,429,440,455,288,430,292,441,452,427,293,442,450,428,443,291,451,426,444,436,422,295,445,437,420,296,446,435,421,294,432,447,425,298,433,448,423,299,434,449,424,297,459,460,461,458,456,457,465,466,463,464,462,467,666,665,667,664,31,599,572,582,583,597,32,570,584,598,30,571,34,585,595,575,35,586,596,573,587,33,594,574,590,580,567,29,588,581,568,27,589,579,569,28,576,593,566,25,577,591,564,26,578,592,565,24,557,555,556,553,554,552,563,561,558,559,560,562,674,673,675,672 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#df8d5557b781bba61b7abe058eca13be711d66cc8eaff0dccefd52d205bc7b58, 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 21:13:06 · history