Equation 677 Database

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Magma c9204c96b6e4…

magma c9204c96b6e4
Size
705
Isomorphism class hash
c9204c96b6e46ee98781f554398bec07b8b2b5b40566fd502ad976407f6dc106
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 20:00:00
Display reorder
660,631,630,632,633,634,635,628,629,627,624,625,626,497,495,496,493,494,492,503,501,502,499,500,498,114,115,116,117,118,119,112,113,111,108,109,110,96,97,98,99,100,101,102,103,104,105,106,107,387,388,389,386,384,385,393,394,395,392,390,391,676,680,685,700,336,338,337,341,339,340,344,342,343,347,345,346,183,184,185,182,180,181,189,190,191,188,186,187,212,210,211,215,213,214,207,208,209,206,204,205,192,193,194,195,196,197,198,199,200,201,202,203,541,542,540,544,545,543,547,548,546,550,551,549,686,692,697,704,127,126,128,129,130,131,124,125,123,120,121,122,382,383,381,378,379,380,373,374,372,376,377,375,621,622,623,620,618,619,612,613,614,615,616,617,6,7,8,9,10,11,4,5,3,1,0,2,486,487,488,489,490,491,484,485,483,480,481,482,665,670,673,677,645,647,646,643,644,642,638,636,637,641,639,640,310,311,309,306,307,308,301,302,300,304,305,303,559,560,558,562,563,561,557,555,556,553,554,552,68,66,67,71,69,70,63,64,65,62,60,61,348,349,350,351,352,353,354,355,356,357,358,359,674,682,683,691,566,565,564,568,569,567,571,572,570,574,575,573,370,371,369,366,367,368,361,362,360,364,365,363,13,14,12,16,17,15,19,20,18,22,23,21,26,24,25,29,27,28,32,30,31,35,33,34,648,649,650,651,652,653,654,655,656,657,658,659,689,693,699,702,162,164,163,167,165,166,159,160,161,158,156,157,460,461,459,456,457,458,466,467,465,462,463,464,427,428,426,430,431,429,425,423,424,421,422,420,408,409,410,411,412,413,414,415,416,417,418,419,599,597,598,595,596,594,590,588,589,593,591,592,688,694,696,703,245,244,243,240,241,242,250,251,249,246,247,248,265,266,264,268,269,267,271,272,270,274,275,273,253,254,252,256,257,255,259,260,258,262,263,261,36,37,38,39,40,41,42,43,44,45,46,47,231,232,233,230,228,229,237,238,239,236,234,235,661,662,663,669,400,399,401,398,396,397,405,406,407,404,402,403,525,526,527,524,522,523,516,517,518,519,520,521,59,57,58,55,56,54,50,48,49,53,51,52,321,322,323,320,318,319,312,313,314,315,316,317,504,505,506,507,508,509,510,511,512,513,514,515,675,679,684,690,604,603,605,602,600,601,609,610,611,608,606,607,468,469,470,471,472,473,474,475,476,477,478,479,155,153,154,151,152,150,146,144,145,149,147,148,133,134,132,136,137,135,139,140,138,142,143,141,440,438,439,443,441,442,435,436,437,434,432,433,687,695,698,701,447,449,448,445,446,444,455,453,454,451,452,450,220,221,219,216,217,218,226,227,225,222,223,224,584,582,583,587,585,586,579,580,581,578,576,577,93,94,95,92,90,91,84,85,86,87,88,89,73,74,72,76,77,75,79,80,78,82,83,81,666,668,672,681,326,325,324,328,329,327,331,332,330,334,335,333,296,294,295,299,297,298,291,292,293,290,288,289,169,170,168,172,173,171,175,176,174,178,179,177,539,537,538,535,536,534,530,528,529,533,531,532,280,281,279,276,277,278,286,287,285,282,283,284,664,667,671,678 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {62} 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 20:00:01 · history