Equation 677 Database

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Magma ec66f961af78…

magma ec66f961af78
Size
705
Isomorphism class hash
ec66f961af7874efff2509b80840d7662c28a60be46c1ae9ac5d737ca4d2667a
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 21:21:48
Display reorder
660,18,258,497,302,324,495,259,19,303,325,20,496,304,257,323,493,21,254,305,320,494,22,255,306,321,492,23,256,307,322,16,300,488,249,330,17,301,486,250,331,15,299,487,248,329,296,12,491,252,326,297,13,489,253,327,298,14,490,251,328,680,685,677,679,355,220,92,170,118,90,218,353,171,119,354,91,172,219,117,88,351,223,173,121,89,352,221,174,122,87,350,222,175,120,346,168,98,215,116,344,169,96,216,114,345,167,97,217,115,164,349,94,214,112,165,347,95,212,113,166,348,93,213,111,669,672,667,662,270,139,473,367,526,471,137,271,365,524,269,472,366,138,525,469,266,135,363,522,470,267,136,364,523,468,268,134,362,521,261,358,464,130,517,262,356,462,128,515,260,357,463,129,516,361,264,467,133,520,359,265,465,131,518,360,263,466,132,519,678,683,686,674,652,27,654,656,659,638,28,636,640,643,644,646,648,29,651,622,620,26,624,627,630,629,24,632,635,614,612,25,616,619,73,382,84,33,601,74,380,82,34,599,75,381,83,35,600,607,605,606,32,608,383,81,85,30,602,384,72,86,31,603,697,703,704,701,574,71,343,183,538,341,69,572,184,536,573,342,182,70,537,339,570,67,186,534,340,571,68,187,535,338,569,66,185,533,565,181,334,62,529,563,179,332,60,527,564,180,333,61,528,177,568,337,65,532,178,566,335,63,530,176,567,336,64,531,692,690,693,695,59,157,514,39,379,512,155,57,40,377,58,513,41,156,378,510,55,153,38,375,511,56,154,36,376,509,54,152,37,374,50,45,505,163,370,48,46,503,161,368,49,47,504,162,369,44,53,508,159,373,42,51,506,160,371,43,52,507,158,372,670,668,663,661,191,232,550,586,408,548,230,192,584,406,193,549,585,231,407,546,190,235,582,404,547,188,233,583,405,545,189,234,581,403,197,577,541,227,399,198,575,539,228,397,199,576,540,229,398,580,196,544,226,402,578,194,542,224,400,579,195,543,225,401,696,694,691,689,420,246,140,283,485,141,247,418,281,483,419,142,282,245,484,143,416,242,279,481,144,417,243,280,482,145,415,244,278,480,411,274,146,237,476,409,272,147,238,474,410,273,148,236,475,277,414,149,240,479,275,412,150,241,477,276,413,151,239,478,676,687,684,681,657,209,658,655,653,642,210,641,639,637,649,650,647,211,645,626,625,208,623,621,634,633,206,631,628,618,617,207,615,613,423,125,500,200,78,421,126,498,201,76,422,127,499,202,77,609,610,611,203,604,124,424,501,204,79,123,425,502,205,80,698,700,702,699,437,103,396,461,562,394,104,435,459,560,436,395,460,102,561,392,433,99,457,558,393,434,100,458,559,391,432,101,456,557,428,452,387,109,553,426,450,385,110,551,427,451,386,108,552,455,431,390,105,556,453,429,388,106,554,454,430,389,107,555,666,664,671,665,598,295,3,316,449,4,293,596,314,447,597,5,315,294,448,2,594,291,319,445,1,595,292,317,446,0,593,290,318,444,589,311,9,286,440,587,312,10,284,438,588,313,11,285,439,310,592,8,289,443,308,590,6,287,441,309,591,7,288,442,675,673,682,688 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#eb741fb6db55479c3e56ca4f84f09a48d9f1cbf15ed347cc0747015cb842acab, 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 21:21:49 · history