Equation 677 Database

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Magma fcb4216d99c9…

magma fcb4216d99c9
Size
705
Isomorphism class hash
fcb4216d99c9bec7a6a21d84ccdf53854cdeb382edd94bb96d23ea9ca58cdb6e
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 16:36:50
Display reorder
660,34,534,60,98,486,35,535,96,61,487,97,536,36,62,488,537,37,101,63,489,538,38,99,64,490,539,39,100,65,491,532,40,66,104,484,533,41,67,102,485,531,42,68,103,483,528,43,69,107,480,529,44,70,105,481,530,45,71,106,482,687,683,686,673,159,342,155,183,82,160,343,184,153,83,185,344,161,154,81,345,158,182,151,78,346,156,180,152,79,347,157,181,150,80,340,165,146,189,73,341,166,144,190,74,339,167,145,191,72,336,164,149,188,76,337,162,147,186,77,338,163,148,187,75,661,672,663,670,194,462,510,84,206,192,463,85,511,204,86,464,193,512,205,465,197,87,513,209,466,195,88,514,207,467,196,89,515,208,460,200,508,90,212,461,198,509,91,210,459,199,507,92,211,456,203,504,93,215,457,201,505,94,213,458,202,506,95,214,682,679,680,684,615,613,614,129,619,623,620,130,622,627,131,628,631,630,635,636,639,128,638,643,645,647,126,646,651,653,655,127,654,659,596,599,597,120,603,604,607,605,121,611,589,591,588,122,595,564,566,565,123,568,573,575,574,124,579,581,583,582,125,587,698,701,703,699,402,294,414,111,390,403,295,112,415,391,113,296,404,416,392,297,405,110,417,393,298,406,108,418,394,299,407,109,419,395,292,400,412,117,388,293,401,413,118,389,291,399,411,119,387,288,396,408,116,384,289,397,409,114,385,290,398,410,115,386,693,692,691,694,450,498,270,217,522,451,499,218,271,523,216,500,452,272,524,501,453,220,273,525,502,454,221,274,526,503,455,219,275,527,496,448,268,223,520,497,449,269,224,521,495,447,267,222,519,492,444,264,226,516,493,445,265,227,517,494,446,266,225,518,666,668,667,662,546,15,258,312,438,547,13,313,259,439,314,14,548,260,440,11,549,315,261,441,12,550,316,262,442,10,551,317,263,443,21,544,256,318,436,19,545,257,319,437,20,543,255,320,435,17,540,252,321,432,18,541,253,322,433,16,542,254,323,434,696,695,689,690,306,330,366,47,474,307,331,48,367,475,46,332,308,368,476,333,309,50,369,477,334,310,51,370,478,335,311,49,371,479,328,304,364,53,472,329,305,365,54,473,327,303,363,52,471,324,300,360,56,468,325,301,361,57,469,326,302,362,55,470,675,681,676,677,612,616,618,171,617,621,624,172,626,625,173,632,629,634,633,640,637,170,642,641,648,644,168,650,649,656,652,169,658,657,600,598,602,177,601,608,606,610,178,609,592,590,594,179,593,570,569,571,176,567,576,572,578,174,577,584,580,586,175,585,700,702,697,704,283,354,140,32,378,284,355,33,138,379,31,356,282,139,380,357,286,28,143,381,358,287,29,141,382,359,285,30,142,383,352,281,135,23,376,353,279,136,24,377,351,280,137,22,375,348,277,134,26,372,349,278,132,27,373,350,276,133,25,374,669,665,664,671,58,249,558,237,426,0,250,238,559,427,239,251,59,560,428,248,3,236,561,429,246,2,234,562,430,247,1,235,563,431,240,7,556,228,424,241,8,557,229,425,242,9,555,230,423,243,6,552,231,420,244,4,553,232,421,245,5,554,233,422,674,678,685,688 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#368900d303714df43b3718b8680935166fd1150994cfe143b7c0fba0a5b985be, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 16:36:51 · history