Equation 677 Database

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Magma e0ee9f54246b…

magma e0ee9f54246b
Size
705
Isomorphism class hash
e0ee9f54246bb514f475a02338b228a94cb6d8aaac032dd0c4188c88924b59be
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 20:33:25
Display reorder
660,577,268,179,377,485,578,269,180,378,486,576,270,376,484,178,271,580,182,380,488,272,581,183,381,489,273,579,181,379,487,274,583,177,383,491,275,584,175,384,492,382,276,582,176,490,277,586,173,386,494,278,587,174,387,495,279,585,172,385,493,661,668,672,670,19,589,94,335,497,17,590,95,336,498,18,588,334,496,96,592,15,97,338,500,593,16,98,339,501,591,14,99,337,499,595,10,92,333,503,596,8,93,331,504,332,594,9,91,502,598,13,88,329,506,599,11,89,330,507,597,12,90,328,505,692,687,690,685,108,621,127,401,205,106,622,128,402,206,107,620,400,207,129,624,111,126,404,204,625,109,124,405,202,623,110,125,403,203,627,103,133,407,196,628,104,134,408,197,406,626,105,135,198,630,102,132,410,199,631,100,130,411,200,629,101,131,409,201,663,669,671,662,553,341,87,317,309,554,342,85,318,307,552,340,316,308,86,344,556,83,320,305,345,557,84,321,306,343,555,82,319,304,347,559,78,323,315,348,560,76,324,313,322,346,558,77,314,350,562,81,326,311,351,563,79,327,312,349,561,80,325,310,674,677,675,680,430,442,55,413,449,431,443,53,414,450,432,444,412,448,54,445,433,51,416,452,446,434,52,417,453,447,435,50,415,451,440,428,46,419,455,441,429,44,420,456,418,439,427,45,454,436,424,49,422,458,437,425,47,423,459,438,426,48,421,457,664,667,665,666,287,194,117,461,529,288,195,115,462,530,286,193,460,528,116,190,290,113,464,532,191,291,114,465,533,192,289,112,463,531,185,285,123,467,535,186,283,121,468,536,466,184,284,122,534,188,281,119,470,538,189,282,120,471,539,187,280,118,469,537,694,697,698,693,524,2,60,70,613,525,3,61,71,614,523,4,69,612,59,5,520,56,73,616,6,521,57,74,617,7,522,58,72,615,1,527,66,68,619,647,644,67,645,646,75,0,526,65,618,653,652,62,654,655,657,656,63,658,659,648,649,64,650,651,703,704,702,701,601,296,22,565,509,602,297,20,566,510,600,295,564,508,21,292,604,25,568,512,293,605,23,569,513,294,603,24,567,511,302,607,28,571,515,303,608,26,572,516,570,301,606,27,514,298,610,31,574,518,299,611,29,575,519,300,609,30,573,517,699,695,696,700,267,153,374,252,162,265,151,375,250,160,266,152,251,161,373,149,263,370,255,165,150,264,371,253,163,148,262,372,254,164,159,258,365,247,168,157,256,366,248,166,249,158,257,364,167,155,261,368,246,171,156,259,369,244,169,154,260,367,245,170,682,673,681,684,541,473,36,389,633,542,474,37,390,634,540,472,388,632,35,476,544,32,392,636,477,545,33,393,637,475,543,34,391,635,479,547,42,395,639,480,548,43,396,640,394,478,546,41,638,482,550,38,398,642,483,551,39,399,643,481,549,40,397,641,676,683,678,679,219,224,136,362,232,217,225,137,363,233,218,223,361,234,138,220,215,139,358,235,221,216,140,359,236,222,214,141,360,237,230,210,142,353,238,231,208,143,354,239,352,229,209,144,240,226,213,145,356,241,227,211,146,357,242,228,212,147,355,243,691,688,689,686 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#bf96e9533ef77c4b1918ac824d690467af6cf34f1d8a49dfc9562b509f0b1543, 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 20:33:26 · history