Equation 677 Database

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Magma de63f0e14052…

magma de63f0e14052
Size
705
Isomorphism class hash
de63f0e14052172351899ad48d9cd10567fc72f2d6f3d71c772212056c9d5280
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 16:35:22
Display reorder
704,142,131,176,165,174,143,166,129,175,130,141,167,138,179,127,164,139,177,128,162,140,178,126,163,171,122,156,133,172,120,157,134,173,121,158,132,125,170,159,136,123,168,160,137,124,169,161,135,153,154,155,152,150,151,144,145,149,147,148,146,681,683,682,680,576,190,567,560,568,577,558,191,569,189,578,559,579,566,186,563,580,564,187,561,581,565,188,562,573,181,555,582,574,182,556,583,575,180,557,584,184,572,554,585,185,570,552,586,183,571,553,587,648,649,650,651,652,653,654,655,658,656,657,659,702,701,700,703,428,7,417,444,418,426,445,8,419,6,427,446,431,416,10,447,429,414,11,448,430,415,9,449,408,5,450,423,409,3,451,424,410,4,452,425,0,411,453,422,2,412,454,420,1,413,455,421,436,437,435,432,433,434,442,443,440,438,439,441,670,669,668,671,392,42,379,367,380,390,368,43,378,44,391,366,395,382,45,370,393,383,46,371,394,381,47,369,377,40,365,387,375,41,363,388,376,39,364,389,36,373,361,386,37,374,362,384,38,372,360,385,356,354,355,359,357,358,351,352,349,350,348,353,677,679,678,676,538,31,527,515,525,539,513,32,526,30,537,514,534,523,34,511,535,524,35,512,536,522,33,510,518,29,506,529,516,27,504,530,517,28,505,528,25,521,509,532,26,519,507,533,24,520,508,531,549,550,551,548,546,547,540,541,545,543,544,542,691,689,688,690,220,645,208,245,209,221,243,646,207,647,219,244,216,204,644,241,217,205,642,242,218,206,643,240,214,636,251,226,215,637,249,227,213,638,250,225,639,210,247,222,640,211,248,223,641,212,246,224,233,231,232,229,230,228,239,237,234,235,236,238,695,692,693,694,476,14,457,492,458,474,493,12,456,13,475,494,479,460,17,495,477,461,15,496,478,459,16,497,463,20,498,471,464,18,499,472,462,19,500,473,23,466,501,470,21,467,502,468,22,465,503,469,483,484,485,482,480,481,489,490,487,488,486,491,661,662,660,663,284,96,271,259,272,282,260,97,270,98,283,258,287,274,99,262,285,275,100,263,286,273,101,261,269,102,257,279,267,103,255,280,268,104,256,281,105,265,253,278,106,266,254,276,107,264,252,277,293,291,292,289,290,288,299,297,294,295,296,298,687,685,684,686,342,113,331,313,332,343,314,111,330,112,344,312,345,334,109,316,346,335,110,317,347,333,108,315,329,119,319,340,327,117,320,341,328,118,318,339,115,325,322,336,116,326,323,337,114,324,321,338,307,308,306,310,311,309,305,303,300,301,302,304,696,698,699,697,57,404,89,74,87,58,72,402,88,403,59,73,56,85,407,77,54,86,405,75,55,84,406,76,95,399,80,48,93,400,78,49,94,401,79,50,398,91,83,51,396,92,81,52,397,90,82,53,67,68,66,70,71,69,65,63,60,61,62,64,664,666,667,665,616,196,604,592,605,617,593,197,603,195,615,591,612,600,192,588,613,601,193,589,614,602,194,590,610,202,598,622,611,203,599,623,609,201,597,621,198,606,594,618,199,607,595,619,200,608,596,620,627,628,629,626,624,625,633,634,631,632,630,635,672,674,675,673 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#35abc55380bad4d0eeaaa3ec3d1bddd8996633b3da151c70fe1eca862e930666, 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 16:35:23 · history