Equation 677 Database

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Magma 0a5cec59788d…

magma 0a5cec59788d
Size
705
Isomorphism class hash
0a5cec59788d1754770e8c0e73397dc738a6f6ff07ae55829856cbb3c92f7dd9
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 21:56:24
Display reorder
660,419,625,136,25,142,417,626,143,137,26,418,624,141,135,24,422,628,145,139,21,420,629,146,140,22,421,627,144,138,23,631,148,134,414,31,632,149,132,415,32,630,147,133,416,30,151,634,130,413,27,152,635,131,411,28,150,633,129,412,29,687,688,686,685,64,493,104,69,183,65,494,184,102,70,63,492,185,103,71,67,489,186,100,72,68,490,187,101,73,66,491,188,99,74,484,181,95,62,75,485,182,93,60,76,483,180,94,61,77,177,487,98,58,78,178,488,96,59,79,179,486,97,57,80,703,704,701,702,260,619,399,237,394,258,620,395,400,238,259,618,393,401,239,256,622,397,402,240,257,623,398,403,241,255,621,396,404,242,617,392,405,251,243,615,390,406,249,244,616,391,407,250,245,388,613,408,254,246,389,614,409,252,247,387,612,410,253,248,671,672,670,669,511,108,89,501,519,512,109,520,87,502,510,110,521,88,503,507,107,522,92,504,508,105,523,90,505,509,106,524,91,506,114,525,84,517,499,115,526,85,518,500,116,527,86,516,498,528,113,83,513,495,529,111,81,514,496,530,112,82,515,497,679,680,678,677,564,300,538,543,576,565,301,577,539,544,566,302,578,537,545,563,299,575,541,546,561,297,573,542,547,562,298,574,540,548,306,567,536,555,549,307,568,534,556,550,308,569,535,557,551,570,305,532,558,552,571,303,533,559,553,572,304,531,560,554,692,691,690,689,213,365,125,599,13,214,363,14,123,597,215,364,12,124,598,216,368,9,128,602,217,366,10,126,600,218,367,11,127,601,360,19,120,219,594,361,20,121,220,595,362,18,122,221,596,15,359,119,222,593,16,357,117,223,591,17,358,118,224,592,699,700,698,697,36,296,267,276,55,37,294,56,268,277,38,295,54,269,278,35,292,51,270,275,33,293,52,271,273,34,291,53,272,274,287,46,265,42,282,285,47,266,43,283,286,45,264,44,284,49,290,261,41,281,50,288,262,39,279,48,289,263,40,280,663,664,662,661,155,638,435,458,430,153,636,431,436,456,154,637,429,437,457,158,641,433,438,454,156,639,434,439,455,157,640,432,440,453,644,428,441,161,449,642,426,442,159,447,643,427,443,160,448,424,647,444,164,452,425,645,445,162,450,423,646,446,163,451,682,683,684,681,379,229,376,8,611,380,230,609,377,6,378,228,610,375,7,656,225,659,658,657,649,226,650,648,651,654,227,655,652,653,235,606,374,385,3,236,607,372,386,4,234,608,373,384,5,605,231,370,381,2,603,232,371,382,1,604,233,369,383,0,695,696,693,694,314,583,338,348,326,312,584,324,336,349,313,582,325,337,350,310,579,322,334,347,311,580,323,335,345,309,581,321,333,346,589,332,344,320,354,590,330,342,318,355,588,331,343,319,356,328,585,340,316,353,329,586,341,317,351,327,587,339,315,352,667,668,665,666,189,171,465,476,212,190,172,210,466,474,191,173,211,467,475,192,174,208,468,472,193,175,209,469,473,194,176,207,470,471,169,203,463,195,482,170,201,464,196,480,168,202,462,197,481,206,165,459,198,478,204,166,460,199,479,205,167,461,200,477,675,676,673,674 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#fd86fc294900b5ccb814b44936109aa3958b6cd4f65ecf12bfe08854715a531f, 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 21:56:25 · history