Equation 677 Database

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Magma 4e491e8b7cd7…

magma 4e491e8b7cd7
Size
705
Isomorphism class hash
4e491e8b7cd7b84b8004c5a5833754acf2a7c42bf9d65804c9efee892d1319c4
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 19:14:48
Display reorder
660,283,379,325,363,327,281,377,323,364,328,282,378,324,362,326,375,279,321,366,330,376,280,322,367,331,374,278,320,365,329,316,385,289,369,333,314,383,287,370,334,315,384,288,368,332,381,319,285,372,336,382,317,286,373,337,380,318,284,371,335,673,685,681,676,47,132,510,116,109,48,130,508,117,110,46,131,509,115,111,128,43,506,119,112,129,44,507,120,113,127,45,505,118,114,516,138,53,122,107,514,136,54,123,108,515,137,52,121,106,134,512,49,125,103,135,513,50,126,104,133,511,51,124,105,666,672,664,669,343,498,553,391,291,341,496,551,389,292,342,497,552,390,290,494,339,549,387,294,495,340,550,388,295,493,338,548,386,293,559,504,349,397,297,557,502,347,395,298,558,503,348,396,296,500,555,345,393,300,501,556,346,394,301,499,554,344,392,299,677,686,683,680,91,407,546,403,14,92,405,544,401,15,93,406,545,402,13,410,94,542,399,17,408,95,543,400,18,409,96,541,398,16,659,654,97,653,652,643,638,98,637,636,651,646,99,645,644,620,623,100,625,624,630,635,101,629,628,411,547,102,404,12,704,697,702,703,206,160,522,240,565,207,158,520,241,563,208,159,521,239,564,163,209,518,236,561,161,210,519,237,562,162,211,517,238,560,528,166,212,231,571,526,164,213,232,569,527,165,214,230,570,169,524,215,234,567,167,525,216,235,568,168,523,217,233,566,689,692,691,690,83,248,255,429,76,84,249,256,427,77,82,250,254,428,78,251,79,258,425,75,252,80,259,426,73,253,81,257,424,74,261,246,89,435,67,262,247,90,433,68,260,245,88,434,69,242,264,85,431,70,243,265,86,432,71,244,263,87,430,72,662,665,661,668,453,183,198,176,225,454,184,199,177,226,452,182,197,178,224,186,449,194,179,228,187,450,195,180,229,185,451,196,181,227,204,189,444,174,223,205,190,445,175,221,203,188,443,173,222,192,200,447,170,219,193,201,448,171,220,191,202,446,172,218,694,695,696,693,7,355,313,417,613,8,353,311,415,611,6,354,312,416,612,351,10,309,413,609,352,11,310,414,610,350,9,308,412,608,304,361,5,423,619,302,359,3,421,617,303,360,4,422,618,357,307,0,419,615,358,305,2,420,616,356,306,1,418,614,678,688,674,675,147,441,488,145,460,148,439,486,143,458,146,440,487,144,459,437,150,491,141,456,438,151,489,142,457,436,149,490,140,455,658,656,153,655,657,642,640,154,639,641,650,648,152,647,649,626,627,156,621,622,632,634,157,631,633,442,492,155,139,461,699,701,700,698,57,601,577,534,479,55,599,575,532,477,56,600,576,533,478,597,60,573,530,475,598,58,574,531,476,596,59,572,529,474,583,607,63,540,485,581,605,61,538,483,582,606,62,539,484,603,579,66,536,481,604,580,64,537,482,602,578,65,535,480,667,663,670,671,22,40,589,467,268,23,41,587,465,266,24,42,588,466,267,39,21,585,463,271,37,19,586,464,269,38,20,584,462,270,595,31,28,473,274,593,32,29,471,272,594,33,30,472,273,34,591,27,469,277,35,592,25,470,275,36,590,26,468,276,679,684,687,682 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#9613877152071542ba1176ebd2d9075b5c9b63b690264e2f5c72257d6a275b00, 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 19:14:49 · history