Equation 677 Database

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Magma 3d4e1433a06f…

magma 3d4e1433a06f
Size
705
Isomorphism class hash
3d4e1433a06fb7b1da32ad7a75e83ec4ff06d42f926636b61aeb678ad88a3e43
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 15:31:09
Display reorder
660,162,507,453,573,531,532,508,163,454,574,533,509,164,455,575,530,161,506,452,572,159,528,504,450,570,529,160,505,451,571,153,498,522,444,564,154,499,523,445,565,155,500,524,446,566,501,156,525,447,567,448,502,157,526,568,503,158,527,449,569,682,684,687,679,311,240,345,381,29,27,241,309,346,382,28,242,310,347,383,25,307,239,344,380,308,26,237,342,378,24,306,238,343,379,302,246,35,336,372,300,247,33,337,373,301,248,34,338,374,245,305,31,339,375,340,243,303,32,376,244,304,30,341,377,670,661,664,663,86,169,369,417,549,550,170,84,370,418,551,168,85,371,419,548,89,165,368,416,87,546,166,366,414,547,88,167,367,415,92,175,540,360,408,90,176,541,361,409,91,174,542,362,410,171,95,543,363,411,364,172,93,544,412,173,94,545,365,413,677,685,676,675,152,637,642,638,640,648,645,150,650,646,656,652,151,658,654,632,148,628,634,630,149,616,613,618,614,624,147,620,626,622,143,133,492,534,140,141,134,493,535,138,142,132,494,536,139,589,146,590,593,592,602,599,144,600,597,607,145,608,610,604,703,697,704,700,270,465,213,41,405,406,466,271,214,39,407,467,272,215,40,404,269,464,216,37,267,402,462,217,38,403,268,463,218,36,261,456,396,219,47,262,457,397,220,45,263,458,398,221,46,459,264,399,222,43,223,460,265,400,44,461,266,401,224,42,691,690,693,689,189,561,98,393,429,430,562,190,96,394,431,563,191,97,395,428,192,560,101,392,193,426,558,99,390,427,194,559,100,391,195,552,420,104,384,196,553,421,102,385,197,554,422,103,386,555,198,423,107,387,105,556,199,424,388,557,200,425,106,389,671,666,665,668,233,280,8,14,114,115,281,231,6,12,116,279,232,7,13,117,236,283,11,17,234,118,284,9,15,119,235,282,10,16,228,278,112,3,20,229,276,113,4,18,230,277,111,5,19,274,227,108,2,23,1,275,225,109,21,273,226,110,0,22,695,692,696,694,181,357,441,519,585,586,358,182,442,520,587,359,180,443,521,584,177,356,440,518,178,582,354,438,516,583,179,355,439,517,187,348,576,432,510,188,349,577,433,511,186,350,578,434,512,351,183,579,435,513,436,352,184,580,514,353,185,581,437,515,674,688,683,678,126,641,639,643,636,644,649,127,647,651,653,657,128,655,659,629,129,633,631,635,130,612,617,615,619,621,131,625,623,627,124,497,137,287,537,125,495,135,285,538,123,496,136,286,539,595,120,594,588,591,598,601,121,596,603,609,122,605,606,611,698,699,701,702,290,489,256,333,319,320,490,288,257,334,318,491,289,255,335,322,293,488,259,332,291,323,486,260,330,321,292,487,258,331,296,480,317,254,324,294,481,315,252,325,295,482,316,253,326,483,299,313,250,327,251,484,297,314,328,485,298,312,249,329,667,672,662,669,74,207,61,477,49,50,208,72,62,478,48,209,73,60,479,52,77,210,64,476,75,53,211,65,474,51,76,212,63,475,80,205,55,67,468,78,206,56,68,469,79,204,54,66,470,201,83,58,70,471,71,202,81,59,472,203,82,57,69,473,681,673,680,686 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#1d08ed48a203bbb312f14b36e229a5f315d68c29c0949a9ef7235ea8d2bd9766, 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 15:31:10 · history