Equation 677 Database

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Magma 4ea8eb88d913…

magma 4ea8eb88d913
Size
705
Isomorphism class hash
4ea8eb88d913f8551444d5bdfd6400d0105ea895fa0494535c91a0a47614921f
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 21:22:46
Display reorder
660,245,94,375,339,459,246,340,95,376,460,96,338,247,374,458,244,97,378,342,462,242,98,379,343,463,243,99,377,341,461,236,373,92,337,457,237,371,93,335,455,238,372,91,336,456,369,239,88,333,453,370,240,89,334,454,368,241,90,332,452,662,665,670,663,351,392,447,232,83,352,230,393,448,84,394,231,350,446,82,354,395,450,235,86,355,396,451,233,87,353,397,449,234,85,349,445,398,227,81,347,443,399,228,79,348,444,400,229,80,441,345,401,226,77,442,346,402,224,78,440,344,403,225,76,685,690,686,687,567,134,387,363,301,568,364,132,388,299,133,362,566,386,300,570,137,390,366,297,571,135,391,367,298,569,136,389,365,296,565,385,140,361,307,563,383,138,359,305,564,384,139,360,306,381,561,143,357,303,382,562,141,358,304,380,560,142,356,302,661,668,671,664,555,171,435,423,411,556,424,172,436,412,170,422,554,434,410,558,174,438,426,414,559,175,439,427,415,557,173,437,425,413,553,433,169,421,409,551,431,167,419,407,552,432,168,420,408,429,549,165,417,405,430,550,166,418,406,428,548,164,416,404,675,674,681,676,507,111,543,11,519,508,12,109,544,520,110,13,506,542,518,510,107,546,10,522,511,108,547,8,523,509,106,545,9,521,505,541,102,17,517,503,539,100,18,515,504,540,101,19,516,537,501,105,16,513,538,502,103,14,514,536,500,104,15,512,672,667,666,669,285,35,277,270,248,286,271,36,275,249,37,269,284,276,250,288,34,273,266,251,289,32,274,267,252,287,33,272,268,253,291,283,41,261,254,292,281,42,262,255,290,282,43,260,256,279,294,40,264,257,280,295,38,265,258,278,293,39,263,259,697,694,695,693,635,154,579,0,145,647,646,152,644,645,153,1,634,578,144,655,157,652,653,654,659,155,656,657,658,651,156,649,648,650,633,573,160,7,151,631,574,158,5,149,632,572,159,6,150,576,629,163,3,147,577,630,161,4,148,575,628,162,2,146,703,701,704,702,112,130,599,207,57,636,208,131,600,637,129,206,113,598,56,640,126,602,210,641,642,127,603,211,643,639,128,601,209,638,114,597,121,205,60,115,595,122,203,58,116,596,120,204,59,593,117,124,201,63,594,118,125,202,61,592,119,123,200,62,696,700,699,698,483,198,495,329,587,484,330,199,496,588,197,331,482,494,586,486,194,498,328,590,487,195,499,326,591,485,196,497,327,589,481,493,189,320,585,479,491,190,321,583,480,492,188,322,584,489,477,192,323,581,490,478,193,324,582,488,476,191,325,580,684,682,678,679,223,46,611,70,471,221,71,44,612,472,45,72,222,610,470,219,49,614,73,474,220,47,615,74,475,218,48,613,75,473,214,609,52,68,469,212,607,50,69,467,213,608,51,67,468,605,217,55,64,465,606,215,53,65,466,604,216,54,66,464,673,677,680,683,22,312,186,531,623,20,532,313,187,624,311,530,21,185,622,25,308,182,534,626,23,309,183,535,627,24,310,184,533,625,28,177,318,529,621,26,178,319,527,619,27,176,317,528,620,180,31,314,525,617,181,29,315,526,618,179,30,316,524,616,688,692,691,689 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#ebc786cbc6f59f4fde563d64e7e77b74986c3576b2c4677bed47ecf46da1acd3, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 21:22:47 · history