Equation 677 Database

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Magma c3b7bff7bbb3…

magma c3b7bff7bbb3
Size
705
Isomorphism class hash
c3b7bff7bbb3362f7d3b1694fa4019c2288be96b21fb0d3fe6ec0b281c30e5a6
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 19:45:53
Display reorder
660,18,374,153,434,386,19,435,375,151,387,20,433,373,152,385,370,21,149,430,382,22,371,150,431,383,23,372,148,432,384,16,380,144,440,392,381,17,142,441,393,15,379,143,439,391,376,12,147,436,388,377,13,145,437,389,378,14,146,438,390,663,665,668,661,256,7,422,398,189,257,399,8,423,187,258,397,6,421,188,10,259,418,394,185,260,11,419,395,186,261,9,420,396,184,254,5,428,404,180,3,255,429,405,178,253,4,427,403,179,0,250,424,400,183,2,251,425,401,181,1,252,426,402,182,690,686,687,689,111,588,482,506,624,109,507,589,483,625,110,505,587,481,623,584,107,478,502,620,108,585,479,503,621,106,586,480,504,622,117,594,488,512,630,595,115,489,513,631,116,593,487,511,629,590,113,484,508,626,591,114,485,509,627,592,112,486,510,628,670,667,672,669,75,263,576,612,201,73,613,264,577,199,74,611,262,575,200,266,71,572,608,197,72,267,573,609,198,70,265,574,610,196,81,269,582,618,192,270,79,583,619,190,80,268,581,617,191,272,77,578,614,195,273,78,579,615,193,271,76,580,616,194,676,681,679,674,82,207,214,410,280,83,411,205,215,281,84,409,206,216,282,203,85,217,406,283,86,204,218,407,284,87,202,219,408,285,88,213,220,416,278,211,89,221,417,279,90,212,222,415,277,209,91,223,412,274,210,92,224,413,275,208,93,225,414,276,662,664,671,666,154,564,600,636,518,155,637,565,601,519,156,635,563,599,517,560,157,596,632,514,158,561,597,633,515,159,562,598,634,516,160,570,606,642,524,571,161,607,643,525,162,569,605,641,523,566,163,602,638,520,567,164,603,639,521,568,165,604,640,522,695,700,699,698,27,36,553,47,530,28,48,37,554,531,29,49,38,552,529,39,26,549,50,526,24,40,550,51,527,25,41,551,52,528,33,42,559,53,536,659,34,658,657,656,35,46,558,57,535,43,32,555,54,532,44,30,556,55,533,45,31,557,56,534,701,703,704,702,105,494,541,231,287,103,229,495,542,288,104,230,493,540,286,490,101,537,227,290,102,491,538,228,291,100,492,539,226,289,96,500,547,237,293,501,94,548,235,294,95,499,546,236,292,496,99,543,233,296,497,97,544,234,297,498,98,545,232,295,693,697,696,694,140,337,346,324,360,141,322,338,347,358,139,323,339,348,359,336,136,349,327,363,137,334,350,325,361,138,335,351,326,362,131,343,352,330,366,344,132,353,328,364,130,345,354,329,365,342,134,355,333,369,340,135,356,331,367,341,133,357,332,368,680,678,673,684,62,243,171,648,446,63,649,241,169,447,61,647,242,170,445,239,58,167,644,442,59,240,168,645,443,60,238,166,646,444,68,249,177,654,452,247,69,175,655,453,67,248,176,653,451,245,64,173,650,448,246,65,174,651,449,244,66,172,652,450,675,683,682,677,122,460,470,314,309,123,315,461,471,307,121,313,462,469,308,463,118,466,310,305,119,464,467,311,306,120,465,468,312,304,128,458,476,320,300,459,129,477,321,298,127,457,475,319,299,454,124,472,316,303,455,125,473,317,301,456,126,474,318,302,692,685,688,691 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#a72914db9cdb367a789c5baa8372a3d5fedd55bc0a2411348ad61481f273a706, 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 19:45:54 · history