Equation 677 Database

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Magma d4f03ea74096…

magma d4f03ea74096
Size
705
Isomorphism class hash
d4f03ea7409677ca5c3602f6627a98c5c00332abbe29d6ea7228d01533404ce2
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 19:49:18
Display reorder
704,92,42,52,63,43,90,53,64,44,91,51,65,95,45,48,62,93,46,49,60,94,47,50,61,40,58,87,69,41,59,88,70,39,57,89,71,54,36,86,68,55,37,84,66,56,38,85,67,83,81,82,79,80,78,74,72,76,77,75,73,683,681,682,680,300,105,314,328,106,301,312,329,107,302,313,327,303,104,317,324,304,102,315,325,305,103,316,326,96,320,306,334,97,318,307,335,98,319,308,333,323,99,309,330,321,100,310,331,322,101,311,332,648,649,650,651,652,653,654,655,658,656,657,659,701,702,700,703,200,631,156,169,632,198,157,170,630,199,158,168,203,634,159,172,201,635,160,173,202,633,161,171,629,162,195,175,627,163,196,176,628,164,197,174,165,625,194,178,166,626,192,179,167,624,193,177,191,189,190,187,188,186,182,180,184,185,183,181,669,670,668,671,563,140,570,538,138,561,571,539,139,562,572,537,559,143,573,534,560,141,574,535,558,142,575,536,135,568,554,529,136,569,552,530,137,567,553,528,564,134,557,532,565,132,555,533,566,133,556,531,546,547,548,549,550,551,544,545,542,540,541,543,679,677,678,676,297,1,260,274,0,298,258,275,2,299,259,273,296,3,263,270,294,4,261,271,295,5,262,272,6,255,288,265,7,256,289,266,8,257,290,264,254,9,291,268,252,10,292,269,253,11,293,267,282,283,284,285,286,287,280,281,278,276,277,279,689,691,688,690,427,28,384,397,29,428,385,398,27,426,386,396,430,24,387,400,431,25,388,401,429,26,389,399,34,390,425,403,35,391,423,404,33,392,424,402,393,30,421,406,394,31,422,407,395,32,420,405,419,417,418,415,416,414,410,408,412,413,411,409,692,695,693,694,235,638,242,210,636,236,240,211,637,234,241,212,238,641,245,213,239,639,243,214,237,640,244,215,644,248,233,208,642,246,231,209,643,247,232,207,251,647,229,204,249,645,230,205,250,646,228,206,219,220,221,218,216,217,225,226,223,224,222,227,662,661,660,663,464,117,478,435,118,462,479,436,119,463,477,437,467,116,474,434,465,114,475,432,466,115,476,433,108,469,459,441,109,470,460,442,110,468,461,443,472,111,458,440,473,112,456,438,471,113,457,439,453,454,455,452,450,451,444,445,449,447,448,446,685,687,684,686,491,128,498,507,126,489,499,508,127,490,500,509,487,131,501,506,488,129,502,504,486,130,503,505,123,496,482,513,124,497,480,514,125,495,481,515,492,122,485,512,493,120,483,510,494,121,484,511,527,525,526,523,524,522,518,516,520,521,519,517,698,696,699,697,605,150,619,582,151,603,620,583,152,604,618,584,601,153,622,585,602,154,623,586,600,155,621,587,148,617,611,580,149,615,609,581,147,616,610,579,613,144,607,576,614,145,608,577,612,146,606,578,593,591,592,589,590,588,599,597,594,595,596,598,666,664,667,665,355,17,361,383,15,356,362,381,16,354,360,382,358,13,364,379,359,14,365,380,357,12,363,378,23,367,353,374,21,368,351,372,22,366,352,373,370,19,349,377,371,20,350,375,369,18,348,376,345,346,347,344,342,343,336,337,341,339,340,338,674,672,675,673 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#adb39c7b26968070fd85ec3ca227f43c35cfd242a3390aaf8597bfe24e1ed89b, 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 19:49:19 · history