Equation 677 Database

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Magma f5d34ecc52b3…

magma f5d34ecc52b3
Size
705
Isomorphism class hash
f5d34ecc52b34a1202f240322d9c798dedc2ef6f0c7f6391a3080583c6a30a0e
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 19:57:58
Display reorder
660,203,111,383,395,517,204,112,384,396,518,202,110,382,394,516,114,206,386,398,520,115,207,387,399,521,113,205,385,397,519,201,117,381,393,515,199,118,379,391,513,200,116,380,392,514,120,197,377,389,511,121,198,378,390,512,119,196,376,388,510,677,684,685,676,303,268,69,504,259,301,269,70,505,260,302,270,68,503,261,271,299,72,507,258,272,300,73,508,256,273,298,71,506,257,294,274,67,502,265,292,275,65,500,266,293,276,66,501,267,277,297,63,498,264,278,295,64,499,262,279,296,62,497,263,667,672,663,668,173,555,432,307,317,174,556,433,308,318,172,554,431,309,316,558,176,435,306,320,559,177,436,304,321,557,175,434,305,319,179,553,430,313,323,180,551,428,314,324,178,552,429,315,322,549,182,426,312,326,550,183,427,310,327,548,181,425,311,325,681,673,687,679,45,623,624,620,621,46,631,632,628,629,44,615,616,612,613,647,48,648,645,644,655,49,656,653,652,639,47,640,637,636,43,607,608,604,605,41,591,592,589,588,42,599,600,596,597,572,39,573,577,576,583,40,584,581,580,412,38,1,134,0,704,702,703,697,125,209,492,3,371,126,210,493,4,372,127,208,491,2,370,212,124,495,6,374,213,122,496,7,375,211,123,494,5,373,131,215,490,9,369,132,216,488,10,367,133,214,489,8,368,218,130,486,12,365,219,128,487,13,366,217,129,485,11,364,692,690,694,693,80,420,37,543,335,81,421,35,544,336,82,419,36,542,334,423,83,33,546,338,424,84,34,547,339,422,85,32,545,337,78,418,28,541,333,79,416,26,539,331,77,417,27,540,332,414,74,31,537,329,415,75,29,538,330,413,76,30,536,328,671,662,664,670,240,90,153,160,444,238,91,154,161,445,239,89,155,159,443,86,243,156,163,447,87,241,157,164,448,88,242,158,162,446,235,96,151,166,442,236,97,152,167,440,237,95,150,165,441,92,234,147,169,438,93,232,148,170,439,94,233,149,168,437,695,691,696,689,185,55,347,109,567,186,53,348,107,568,184,54,346,108,566,51,188,350,105,570,52,189,351,106,571,50,187,349,104,569,191,61,345,100,565,192,59,343,98,563,190,60,344,99,564,57,194,341,103,561,58,195,342,101,562,56,193,340,102,560,683,688,675,674,246,622,627,625,626,244,630,635,633,634,245,614,619,617,618,646,249,651,649,650,654,247,659,657,658,638,248,643,641,642,252,606,611,609,610,250,590,595,593,594,251,598,603,601,602,578,255,579,574,575,582,253,587,585,586,171,254,535,509,522,700,701,698,699,136,468,284,15,353,137,469,285,16,354,135,467,283,14,352,471,139,280,18,356,472,140,281,19,357,470,138,282,17,355,142,466,290,21,359,143,464,291,22,360,141,465,289,20,358,462,145,286,24,362,463,146,287,25,363,461,144,288,23,361,661,669,665,666,229,530,407,480,456,230,531,408,481,457,231,529,406,479,455,533,228,410,483,459,534,226,411,484,460,532,227,409,482,458,220,528,405,478,454,221,526,403,476,452,222,527,404,477,453,524,223,401,474,450,525,224,402,475,451,523,225,400,473,449,682,680,686,678 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#b82bea23d952545bcb5d6b6a0cc235694bb3bc5cc3b3a153b6c38e307d02b955, 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 19:57:59 · history