Equation 677 Database

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Magma e78c9f09c3ae…

magma e78c9f09c3ae
Size
705
Isomorphism class hash
e78c9f09c3aedbee40a9df0180ede96806768ddcf4ccb9680d9fe12cbd61450f
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 20:05:43
Display reorder
704,68,88,75,37,76,66,38,89,77,87,67,36,84,74,71,40,85,72,69,41,86,73,70,39,63,94,43,81,95,64,44,82,65,93,42,83,90,62,46,80,91,60,47,78,92,61,45,79,51,52,53,50,48,49,57,58,55,56,54,59,683,680,682,681,580,23,30,98,31,581,96,21,32,22,579,97,19,33,576,101,20,34,577,99,18,35,578,100,586,14,104,28,12,587,102,29,585,13,103,27,17,582,107,24,15,583,105,25,16,584,106,26,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,509,484,471,236,472,507,234,485,473,483,508,235,480,470,505,239,481,468,506,237,482,469,504,238,515,490,231,477,491,513,232,478,514,489,233,479,486,511,230,476,487,512,228,474,488,510,229,475,499,500,498,502,503,501,497,495,492,493,494,496,669,671,668,670,195,171,207,419,208,196,417,172,209,173,197,418,170,206,194,415,168,204,192,416,169,205,193,414,201,177,410,213,178,202,408,214,203,179,409,215,176,200,413,212,174,198,411,210,175,199,412,211,185,183,184,181,182,180,191,189,186,187,188,190,679,676,678,677,528,552,550,292,551,529,293,553,549,554,530,291,555,546,531,288,556,547,532,289,557,548,533,290,534,558,298,541,559,535,299,542,536,560,297,540,561,537,294,544,562,538,295,545,563,539,296,543,574,575,573,570,571,572,565,566,567,568,569,564,689,690,688,691,300,325,322,638,323,301,636,326,321,324,302,637,328,318,303,641,329,319,304,639,327,320,305,640,306,331,644,313,332,307,642,314,308,330,643,312,334,309,647,316,335,310,645,317,333,311,646,315,340,341,339,336,337,338,346,347,344,342,343,345,692,694,693,695,267,248,279,520,280,268,521,246,281,247,269,519,251,278,266,516,249,276,264,517,250,277,265,518,273,243,526,285,244,274,527,286,275,245,525,287,242,272,522,284,240,270,523,282,241,271,524,283,257,255,256,253,254,252,263,261,258,259,260,262,661,662,660,663,140,108,147,356,148,138,354,109,149,110,139,355,111,146,143,359,112,144,141,357,113,145,142,358,135,114,351,153,115,136,352,154,137,116,353,155,117,134,350,152,118,132,348,150,119,133,349,151,131,129,130,127,128,126,122,120,124,125,123,121,685,686,684,687,381,405,390,163,391,382,164,406,392,407,383,162,404,393,380,166,402,394,378,167,403,395,379,165,372,396,161,388,397,373,159,389,374,398,160,387,399,375,157,384,400,376,158,385,401,377,156,386,368,366,367,371,369,370,363,364,361,362,360,365,698,697,699,696,451,420,457,227,458,452,225,421,456,422,450,226,423,460,454,223,424,461,455,224,425,459,453,222,449,426,218,463,427,447,216,464,448,428,217,462,429,445,221,466,430,446,219,467,431,444,220,465,442,443,441,438,439,440,433,434,435,436,437,432,666,665,667,664,601,635,617,5,615,602,3,633,616,634,600,4,631,613,604,0,632,614,605,2,630,612,603,1,607,626,11,623,624,608,9,621,606,625,10,622,629,610,7,619,627,611,8,620,628,609,6,618,594,595,596,597,598,599,592,593,590,588,589,591,674,673,675,672 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#b8eeccb61bf3cf52a025c1a85426255b55158ec212ce139ae8ac4787df68c2e8, 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 20:05:44 · history