Equation 677 Database

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Magma 5045491fed79…

magma 5045491fed79
Size
705
Isomorphism class hash
5045491fed7970ab69b38365319543820255e4ee0f169d50be746974a51f0c01
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 16:51:56
Display reorder
660,562,418,252,358,304,563,419,305,253,359,303,417,561,254,357,558,414,300,255,354,559,415,301,256,355,560,416,302,257,356,310,409,258,553,349,311,410,259,554,350,309,408,260,552,348,412,306,261,556,352,413,307,262,557,353,411,308,263,555,351,686,678,675,684,112,218,33,430,212,110,216,210,31,431,211,217,111,32,429,115,221,215,29,426,113,219,213,30,427,114,220,214,28,428,207,224,39,107,421,208,222,37,108,422,209,223,38,109,420,227,206,35,106,424,225,204,36,104,425,226,205,34,105,423,666,672,664,661,506,334,86,406,313,507,335,314,87,407,312,333,505,88,405,502,330,316,89,402,503,331,317,90,403,504,332,315,91,404,319,325,84,497,397,320,326,85,498,398,318,324,83,496,396,328,322,80,500,400,329,323,81,501,401,327,321,82,499,399,682,673,677,674,644,647,127,650,648,652,655,656,125,658,640,639,636,126,642,612,615,616,123,618,620,623,624,124,626,628,631,632,122,634,521,0,118,79,565,522,2,116,77,566,520,1,117,78,564,597,598,121,600,601,607,608,119,605,610,3,523,120,76,567,703,697,700,704,272,370,145,250,10,270,371,11,143,251,12,369,271,144,249,275,366,13,141,246,273,367,14,142,247,274,368,15,140,248,8,361,151,267,241,9,362,149,268,242,7,360,150,269,240,364,4,147,266,244,365,5,148,264,245,363,6,146,265,243,692,690,689,693,346,49,237,70,518,347,50,519,238,71,517,51,345,239,72,342,48,514,236,73,343,46,515,234,74,344,47,516,235,75,509,40,228,337,68,510,41,229,338,69,508,42,230,336,67,43,512,231,340,64,44,513,232,341,65,45,511,233,339,66,662,667,670,669,192,173,277,176,163,193,174,161,278,177,162,175,191,276,178,188,172,159,280,179,189,170,160,281,180,190,171,158,279,181,154,164,283,198,182,152,165,284,199,183,153,166,282,197,184,167,157,286,194,185,168,155,287,195,186,169,156,285,196,187,691,695,696,694,582,594,288,466,550,583,595,551,289,467,549,593,581,290,465,578,590,546,291,462,579,591,547,292,463,580,592,548,293,464,541,585,294,573,457,542,586,295,574,458,540,584,296,572,456,588,544,297,576,460,589,545,298,577,461,587,543,299,575,459,687,688,680,685,651,645,20,646,649,659,653,657,21,654,641,637,643,19,638,619,613,617,16,614,627,621,625,17,622,635,629,633,18,630,537,203,26,569,482,538,201,27,570,480,536,202,25,568,481,602,603,22,599,596,604,609,23,611,606,200,539,24,571,483,701,698,702,699,494,454,102,128,394,495,455,395,103,129,393,453,493,101,130,490,450,390,98,131,491,451,391,99,132,492,452,392,100,133,385,445,93,485,134,386,446,94,486,135,384,444,92,484,136,448,388,96,488,137,449,389,97,489,138,447,387,95,487,139,668,665,671,663,478,534,55,442,382,479,535,383,56,443,381,533,477,57,441,474,530,378,54,438,475,531,379,52,439,476,532,380,53,440,373,525,61,469,433,374,526,62,470,434,372,524,63,468,432,528,376,60,472,436,529,377,58,473,437,527,375,59,471,435,681,683,679,676 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#41328e14760452489c50b79fcc49c074869181cbfbd0a816da081f28123ef346, 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 16:51:58 · history