Equation 677 Database

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Magma 64729e90bcaa…

magma 64729e90bcaa
Size
705
Isomorphism class hash
64729e90bcaab50be032e66aff296cec3ac88e66a14a5003b1daef6188af2fa7
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 16:37:54
Display reorder
660,617,618,604,66,608,624,638,637,67,628,657,658,68,648,644,598,597,584,69,588,558,557,544,70,548,578,577,564,71,568,424,437,64,438,428,444,455,65,456,448,464,477,63,478,468,497,484,60,498,488,517,504,61,518,508,537,524,62,538,528,694,692,689,701,612,600,609,156,611,629,620,632,157,631,652,641,158,651,649,581,592,589,159,591,540,552,549,160,551,561,572,569,161,571,429,432,162,420,431,449,451,163,441,450,469,472,164,461,471,492,489,165,480,491,512,509,166,500,511,532,529,167,521,531,702,699,695,686,357,174,184,28,211,185,175,358,29,212,359,176,27,210,183,177,356,180,24,214,178,354,181,25,215,179,355,182,26,213,190,348,34,172,209,191,349,35,173,207,189,350,33,171,208,351,186,30,168,205,352,187,31,169,206,353,188,32,170,204,668,671,680,666,298,48,2,103,309,1,49,299,104,310,297,50,102,311,0,51,294,5,106,308,52,295,3,107,306,53,296,4,105,307,8,289,101,54,300,6,290,99,55,301,7,288,100,56,302,292,11,97,57,303,293,9,98,58,304,291,10,96,59,305,663,677,664,676,610,616,607,72,603,627,636,630,73,623,650,656,74,643,647,596,590,587,75,583,556,550,547,76,543,576,570,567,77,563,427,430,78,436,423,447,458,79,459,457,467,470,80,476,463,490,487,81,496,483,510,507,82,516,503,530,527,83,536,523,697,687,693,690,615,601,619,12,613,639,621,635,13,633,655,640,14,653,659,580,595,599,15,593,541,555,559,16,553,560,575,579,17,573,439,435,18,421,433,440,454,19,442,452,479,475,20,460,473,495,499,21,481,493,515,519,22,501,513,535,539,23,520,533,703,700,691,704,602,606,605,229,614,625,626,622,230,634,642,646,228,654,645,586,582,585,232,594,546,542,545,233,554,566,562,565,231,574,425,422,235,426,434,445,443,236,446,453,465,462,234,466,474,482,485,238,486,494,502,505,239,506,514,522,525,237,526,534,688,696,698,685,417,91,285,192,267,286,92,418,193,268,419,90,194,269,287,94,416,284,195,266,95,414,282,196,264,93,415,283,197,265,276,408,198,89,273,277,409,199,87,274,278,410,200,88,275,411,279,201,85,272,412,280,202,86,270,413,281,203,84,271,681,684,669,661,345,393,39,226,112,40,394,346,227,113,347,395,225,111,41,392,344,38,222,108,390,342,36,223,109,391,343,37,224,110,45,336,217,384,118,46,337,218,385,119,47,338,216,386,117,339,44,220,387,114,340,42,221,388,115,341,43,219,389,116,678,670,683,675,381,369,333,147,321,334,370,382,148,322,383,371,149,323,335,368,380,332,146,320,366,378,330,144,318,367,379,331,145,319,324,372,153,360,312,325,373,154,361,313,326,374,155,362,314,375,327,152,363,315,376,328,150,364,316,377,329,151,365,317,672,674,665,667,405,263,131,136,250,129,261,406,137,251,407,262,135,249,130,259,404,127,132,246,260,402,128,133,247,258,403,126,134,248,122,396,142,254,241,120,397,143,252,242,121,398,141,253,240,399,125,138,257,244,400,123,139,255,245,401,124,140,256,243,673,679,662,682 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#37e131d0061e11ac6a08c1b5043c4a4bd1e23715ce44e1796d2c3958c15ae4cf, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 16:37:56 · history